Democratic presidential front-runner Hillary ClintonHillary Diane Rodham ClintonPavlich: Mueller’s indictment of the media Poll shows 36 percent support Trump's reelection, 43 percent prefer generic Democrat How the Clinton machine flooded the FBI with Trump-Russia dirt … until agents bit MORE should not pick a senator from a Republican-controlled state as her vice president, Senate Minority Leader Harry ReidHarry Mason ReidHow the Clinton machine flooded the FBI with Trump-Russia dirt … until agents bit Senate Republicans eye rules change to speed Trump nominees Harry Reid knocks Ocasio-Cortez's tax proposal: Fast 'radical change' doesn't work MORE (D-Nev.) warned Monday. 

"If we have a Republican governor in any of those states, the answer is not only no, but hell no. I would do whatever I can, and I think most of my Democratic colleagues here would say the same thing," Reid told MSNBC's "AM Joy" when asked about the possibility of Democratic Sens. Elizabeth WarrenElizabeth Ann WarrenPoll shows 36 percent support Trump's reelection, 43 percent prefer generic Democrat Trump's approval rating holds steady at 45 percent amid government shutdown: poll Senate Dems introduce bill to keep DACA info private MORE (Mass.) or Sherrod BrownSherrod Campbell BrownOregon Dem top recipient of 2018 marijuana industry money, study finds 2020 Democrats barnstorm the country for MLK weekend Sen. Casey says he won't run for president in 2020 MORE (Ohio) being named Clinton's No. 2. 
 
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Reid added that he would "yell and scream to stop that." 
 
Democrats are fighting to regain control of the Senate majority this election cycle. They'll need a net gain of four seats to win back the chamber if they retain the White House, and a net gain of five seats to win the Senate back outright. 
 
While the 2016 map is tilted in favor of Senate Democrats — they are defending 10 Senate seats, compared to 24 for Republicans — a net gain of five seats is an uphill climb.
 
Both Warren and Brown, as well as Sen. Cory Booker (D-N.J.), are considered potential VP picks for Clinton and hail from states with Republican governors. If one of them were picked for vice president and Clinton won the White House, they would need to step down.
 
That could pave the way for a GOP governor to temporarily appoint a Republican to fill a Senate seat, forcing Democrats to win an extra seat to reclaim the majority. 
 
Brown, who has said he doesn't want to be vice president, has said that he's worried about allowing Republican Ohio Gov. John Kasich to fill his seat. 
 
"If I were on the ticket and Hillary were to win, that John Kasich would nominate and would appoint my successor, and that bothers me so," he told MSNBC's "Hardball" earlier this month.
 
Sen. Tim KaineTimothy (Tim) Michael KaineMcConnell blocks bill to temporarily reopen DHS Trump pitches new plan to reopen government amid Dem pushback Democrats signal they'll reject Trump shutdown proposal MORE (D-Va.) is also considered a potential vice presidential pick for Clinton. The governor of his home state, Terry McAuliffe, is a Democrat and a longtime ally of Clinton. Virginia's other senator, Mark WarnerMark Robert WarnerHillicon Valley: Lawmakers worry as 'deepfakes' spread | New intel strategy sees threats from emerging tech | Google fined M under EU data rules | WhatsApp moves to curb misinformation On The Money: Shutdown Day 32 | Senate to vote on dueling funding measures | GOP looks to change narrative | Dems press Trump on recalled workers | Kudlow predicts economy will 'snap back' after shutdown Overnight Energy: Polls highlight growing worries about climate change | Watchdog asked to probe recall of furloughed Interior workers | Canada allows preliminary work on Keystone XL MORE (D-Va.), could also be a contender.
 
But many have speculated that Brown or Warren would be stronger picks for Clinton, who may need to find a running mate that excites the liberal base after her bruising primary battle with Sen. Bernie SandersBernard (Bernie) SandersPoll shows 36 percent support Trump's reelection, 43 percent prefer generic Democrat Trump's approval rating holds steady at 45 percent amid government shutdown: poll Senate Dems introduce bill to keep DACA info private MORE (I-Vt.).  
 
Warren and Brown are beloved by the left, party for their willingness to oppose trade deals and battle with Wall Street.
 
Updated at 1:21 p.m.