Trump eyes House members for Cabinet jobs

President-elect Donald TrumpDonald John TrumpMilitary personnel to handle coronavirus patients at facilities in NYC, New Orleans and Dallas Navy hospital ship USNS Comfort has total of 20 patients: report Fauci says that all states should have stay-at-home orders MORE has already tapped one House lawmaker for a key post in his fledgling administration: Conservative Rep. Mike Pompeo (R-Kan.) is likely to be the next CIA director.

But other relatively obscure House lawmakers — including GOP Reps. Cathy McMorris RodgersCathy McMorris RodgersOvernight Energy: Trump rolls back Obama-era fuel efficiency standards | Controversial Keystone XL construction to proceed | Pressure mounts to close national parks amid pandemic Critics blast Trump mileage rollback, citing environment and health concerns The myth about Puerto Rican statehood that won't go away MORE (Wash.), Tom Price (Ga.), Mike McCaul (Texas) and Marsha BlackburnMarsha BlackburnTrump must cut our dependence on Chinese drugs — whatever it takes Senate passes House's coronavirus aid bill, sending it to Trump Nikki Haley expected to endorse Loeffler in Senate race MORE (Tenn.) — could make the leap from lower chamber to presidential Cabinet.

There’s plenty of precedent for president-elects to bring House members into their inner circle. After Barack ObamaBarack Hussein ObamaThe Hill's Campaign Report: Coronavirus forces Democrats to postpone convention Biden associates reach out to Holder about VP search Poll: More Republican voters think party is more united than Democratic voters MORE won the White House in 2008, he named Rep. Rahm Emanuel (D-Ill.) his first chief of staff. Obama also picked Rep. Hilda Solis (D-Calif.) to lead the Labor Department and Rep. Ray LaHood, a Republican from his home state of Illinois, to run his Transportation Department.

Several House lawmakers have already joined the parade of Cabinet job seekers who’ve lined up in recent days at Trump Tower in New York City and Trump National Golf Club in Bedminster, N.J.

House Financial Services Committee Chairman Jeb Hensarling (R-Texas), who’s been mentioned as a possible Treasury secretary, paid Trump a visit last week to talk about tax policy, trade and repealing Dodd-Frank financial regulations. McMorris Rodgers, the highest-ranking Republican woman in Congress, huddled with Trump over the weekend in Bedminster. Retiring Rep. Cynthia LummisCynthia Marie LummisCheney's decision not to run for Senate sparks Speaker chatter Liz Cheney decides against Senate bid in Wyoming Liz Cheney leads GOP field by 20 points in potential Wyoming Senate race: poll MORE (R-Wyo.) dropped by to see Trump on Tuesday.

It’s also possible that Trump could recruit House members for ambassadorships. Retiring Rep. Matt SalmonMatthew (Matt) James SalmonArizona voters like Kyl but few think he'll stick around Former Sen. Jon Kyl to replace McCain in Senate Arizona governor faces pressure over McCain replacement MORE (R-Ariz.), for example, is chairman of the Foreign Affairs subcommittee on Asia and the Pacific and the only Republican in Congress who’s fluent in Mandarin. Some of his colleagues have mentioned Salmon as a possible ambassador to China.

While the list is not comprehensive, here are a handful of House members who could land a spot in the Trump Cabinet:

Rep. Tom Price (R-Ga.)

Price, the current Budget Committee chairman and a former orthopedic surgeon, is a top contender to become Trump’s Health and Human Services secretary, sources said. It’s a job that would place him right in the middle of the GOP’s effort to repeal and replace ObamaCare.

A vocal critic of the Affordable Care Act, Price last year authored his own repeal and replace legislation that includes fewer dollars for high-risk pools — $3 billion — than other proposals, according to a Vox analysis.

Price also helped shape the healthcare plank for the House GOP’s “Better Way” agenda.

Like Vice President-elect Mike PenceMichael (Mike) Richard PenceMilitary personnel to handle coronavirus patients at facilities in NYC, New Orleans and Dallas Kushner makes first appearance at coronavirus briefing Meadows sets up coronavirus hotline for members of Congress MORE, Price served in the past as chairman of the conservative Republican Study Committee. And like Pence, Price would serve as a link between the Trump White House and GOP leaders on Capitol Hill.

Given his committee work, Price also could easily step into the role of director of the Office of Management and Budget, which is responsible for producing the president’s annual budget. Price met with Trump in New York just last week.

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Rep. Cathy McMorris Rodgers (R-Wash.)

Trump’s first five picks for his administration — Reince Priebus, Stephen Bannon, Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsThe Hill's Campaign Report: Coronavirus forces Democrats to postpone convention Roy Moore to advise Louisiana pastor arrested for allegedly defying ban on large gatherings Trump campaign demands Sessions stop implying he has president's support MORE (R-Ala.), retired Lt. Gen. Michael Flynn and Pompeo — have all been white men, but he’s vowed that women will fill key slots in his Cabinet.

McMorris Rodgers, the House Republican Conference chairwoman and the only woman on either the House or Senate GOP leadership teams, is one possibility.

Like Speaker Paul RyanPaul Davis RyanWho should be the Democratic vice presidential candidate? The Pelosi administration It's not populism that's killing America's democracy MORE (R-Wis.), McMorris Rodgers hesitated to endorse Trump once it was clear he would win the nomination. She had been uneasy about some of his past comments about women, and as the mother of a son with Down syndrome, she didn’t appreciate a 2015 video of Trump apparently mocking a disabled reporter.

But a meeting on Capitol Hill in May appeared to smooth things over, and McMorris Rodgers, the No. 4 House GOP leader, soon publicly endorsed the billionaire businessman and reality TV star.

The two met face to face again on Sunday in Bedminster. The Trump campaign said the discussion centered on a host of issues: how to optimize federal lands, energy exploration, mining, working families and greater access to services for children with special needs.

Those clues could mean Trump is considering her for Interior, Energy or Labor secretary.

Another GOP woman who could find herself in the Cabinet is Blackburn, a Tennessee conservative who leads the special House committee investigating Planned Parenthood. Blackburn is a top Trump ally who was named this month to his transition team's executive committee.

Both Blackburn and McMorris Rodgers serve on the Energy and Commerce Committee.

“Both Blackburn and McMorris Rodgers have distinguished careers as public leaders and subject matter expertise, and would bring diversity to the Cabinet,” said one House colleague who knows both women.

Rep. Mike McCaul (R-Texas)

McCaul, the House Homeland Security chairman for the past four years, is mulling a primary challenge to Sen. Ted CruzRafael (Ted) Edward CruzFlorida sheriff asks for new leads in disappearance of Carole Baskin's former husband after Netflix's 'Tiger King' drops Ted Cruz jokes about quarantine boredom, 'Tiger King' Trump faces mounting pressure to unleash Defense Production Act MORE (R-Texas). But if offered the Homeland Security secretary post, McCaul has indicated he’d jump at the opportunity.

The challenge for the ambitious Texan is that he has some tough competition. Trump is also looking at retired Marine Gen. John F. Kelly and Frances Townsend, a homeland security and counterterrorism expert who served in the George W. Bush administration, according to The Washington Post.

And Trump met this weekend with Kansas Secretary of State Kris Kobach, an anti-immigration hard-liner who made a national name for himself authoring Arizona’s tough immigration law known as SB 1070. Before his meeting with Trump, Kobach was spotted holding his written plan for DHS, including a line that read “extreme vetting questions for high-risk aliens.”

McCaul, a frequent guest on the Sunday shows, published a book in January titled “Failures of Imagination.” In it, he highlights points of vulnerabilities, including cyber and biological warfare. The artwork on his book cover: smoke billowing from the U.S. Capitol complex.

The Homeland Security Committee chairman advised Trump on national security issues during the 2016 campaign. Retiring House Veteran Affairs Committee Chairman Jeff Miller (R-Fla.) also was part of Trump’s national security team and has been floated as a possible Veteran Affairs secretary.

Rep. Tulsi GabbardTulsi Gabbard20 House Dems call on Trump to issue two-week, nationwide shelter-in-place order The Hill's Morning Report — ,000,000,000,000: GOP unveils historic US rescue effort Gillibrand endorses Biden for president MORE (D-Hawaii)

“Shocked” is how one House Democrat described her reaction when she learned that Gabbard had met with Trump on Monday. But the rising Democratic star often has had that effect on people.

Gabbard also stunned her colleagues earlier this year when she quit her leadership post at the Democratic National Committee and endorsed Sen. Bernie SandersBernie SandersHuffPost political reporter on why Bernie fell way behind Biden Schumer: Administration 'must move heaven and earth' to implement new unemployment benefits Biden associates reach out to Holder about VP search MORE (I-Vt.) over Hillary ClintonHillary Diane Rodham ClintonFormer Obama adviser Plouffe predicts 'historical level' of turnout by Trump supporters Poll: More Republican voters think party is more united than Democratic voters Whoopi Goldberg presses Sanders: 'Why are you still in the race?' MORE in the Democratic presidential primary.

An Army veteran of the Iraq War who serves on both the Armed Services and Foreign Affairs committees, Gabbard was reportedly in the running to be Trump’s ambassador to the United Nations. But Trump tapped South Carolina Gov. Nikki Haley (R) for the U.N. post instead late Tuesday night.

Gabbard would be an interesting pick for Trump. She would provide both gender and racial diversity: She’s the first American-Samoan woman elected to Congress and the first Hindu member of Congress. At 35, she’s also a millennial who co-chairs the Congressional Future Caucus. And her nomination would show Trump’s willingness to reach across the aisle.

“She is clearly someone who always puts people before politics,” said Missouri Rep. Jason Smith, a new member of the GOP leadership team who belongs to a bipartisan workout group with Gabbard.

In a statement, Gabbard said she agreed to meet with Trump to discuss U.S. policy in Syria and the fight against the Islamic State in Iraq and Syria.

“This was an opportunity to advocate for peace,” she wrote in a lengthy post on Medium, “and I felt it was important to take the opportunity to meet with the President-elect to counteract neocons’ steady drumbeats of war, which threaten to drag us into an escalation of the war to overthrow the Syrian government.”

Sarah Ferris contributed to this report, which was updated at 7:51 a.m.