Their language would grant immediate provisional residency status to millions of illegal residents, which some Republicans will oppose despite the extra border funds.

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But the boost to border enforcement seems likely to win over several Republicans, and may even allow the bill to pass with 70 votes in the Senate. That's a goal set by supporters of the bill who want to ensure it has a chance of passing in the House.

A few personnel issues will develop around the Senate, including one involving Senate membership — next week will decide who will replace Secretary of State John KerryJohn KerryWith help from US, transformative change in Iran is within reach Ellison comments on Obama criticized as 'a stupid thing to say' 'Can you hear me now?' Trump team voices credible threat of force MORE in the Senate. Rep. Ed MarkeyEd MarkeyDem senators ask Bannon for more info about Breitbart contact Dem lawmaker: FCC now stands for 'Forgetting Choice and Competition' Senate Dems want Trump to release ethics waivers, visitor logs MORE (D-Mass.) is well ahead in most polls, and is expected to defeat Gabriel Gomez in the Massachusetts special election on Tuesday.

In addition, senators will vote on the nomination of Charlotte, North Carolina Mayor Anthony FoxxAnthony FoxxDC mayor touts progress in reducing traffic deaths Toll roads poised to boom under Trump plan Transportation chief urges Trump to press forward on self-driving cars MORE as Secretary of Transportation, and businesswoman Penny PritzkerPenny PritzkerDeVos should ‘persist’ despite liberal opposition Indiana teachers hold sit-in to demand Young recuse himself from DeVos vote Overnight Tech: Trump team eyes FCC overhaul | AT&T chief says no plans to spin off CNN in merger | Commerce pick heads to hearing MORE as Secretary of Commerce.

The Senate may also try to find a way forward on a bill to avoid a doubling of student loan interest rates. The House has passed a bill that Republicans say is close to a plan President Obama supports.

The Senate has not passed anything yet, which is putting pressure on the upper chamber to get something done before the rates double on July 1. In the meantime, House GOP leaders have said they are negotiating directly with the Obama administration, and may announce some deal without any help from the Senate.

But the House is not without its own problems. The chamber failed to pass a farm bill that Speaker John BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE (R-Ohio) voted for, leaving it unclear how the House will handle farm policy and prompting questions about whether the GOP will be able to get its own members in line to approve the bill.

Some of the sting from that vote will likely be felt when the House plans to approve a bill funding the Department of Agriculture for 2014, which could come up in the near future.

In the meantime, members of the House will consider two bills aimed at increasing offshore oil production. Republicans have said President Obama has not been aggressive enough in making offshore lease sales, and are looking to expand energy exploration off the Atlantic and Pacific coasts.

Below is a more detailed look at the week ahead:

Monday


The Senate starts at noon, and at 5:30 p.m. will hold a vote to end debate on an amendment from Sen. Patrick LeahyPatrick LeahyLawmakers talk climate for Earth Day, Science March Poll: Sanders most popular senator in the US Senate Dems offer bill to restore internet privacy rules MORE (D-Vt.) that includes the Corker-Hoeven proposals and other changes to S. 744.

The Senate then hopes to get into a position to vote on that substitute amendment during the week, and then pass the bill by Friday at the latest, just before leaving for the July 4 week.

The House meets only for a pro-forma session at 11 a.m., but no votes are expected.

Tuesday

The House starts at noon, and will consider up to four suspension bills. Any needed roll call votes on these bills will be held at 6:30 p.m. (we never provide links to bills that name buildings and infrastructure):

— H.R. 2383, designating a bridge connecting St. Louis and Illinois as the Stan Musial Veterans Memorial Bridge

— H.R. 1092, naming an air traffic control center in Nashua, New Hampshire as the Patricia Clark Boston Air Route Traffic Control Center.

— H.R. 2289, renaming a section of the Internal Revenue Code as the Kay Bailey Hutchison Spousal IRA

The Senate is in, and will continue work on this day and throughout the week on the immigration bill. Some work on a student loan bill is also possible in the Senate, although there were no firm signs of this as of late Friday.

Wednesday-Thursday

The House meets at noon on both days, and during this time will consider two energy bills and the 2014 agriculture spending bill. The energy bills are:

H.R. 2231, the Offshore Energy and Jobs Act, which would require the administration to expand offshore lease sales on the Atlantic and Pacific coasts.

H.R. 1613, the Outer Continental Shelf Transboundary Hydrocarbon Agreements Authorization Act, which would approve energy production along the U.S.-Mexico maritime border.

The House will also consider another suspension bill at some during during these two days:

H.R. 1864, requiring an Inspector General investigation of allegations of retaliatory personnel actions taken in response to communications on sexual assault.

Friday

The House meets at 9 a.m. to hold any debate and voting that remains from the week.