Sen. Richard Shelby Richard Craig ShelbySenate to push funding bill vote up against shutdown deadline Senate GOP eyes early exit Dems discussing government funding bill into February MORE (R-Ala.) is warning against shutting down the government even as President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE doubles down on a fight over funding the U.S.-Mexico border wall.

"Oh no, I don't think anybody wins on that. I think that's a no-win for both parties. I think Democrats will tell you that, too," Shelby, who chairs the Senate Appropriations Committee, told reporters on Monday evening.

Trump doubled down on his shutdown threat on Monday, saying if he doesn't get the border security measures he wants, he would "have no problem doing a shutdown."

The president said he wants Congress to authorize more funding for his long-desired wall at the U.S. southern border and to pass an overhaul of the nation's immigration system.

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But his rhetoric undercuts GOP leadership on Capitol Hill, who signaled last week that they expected the fight over wall funding to wait until after the November elections.

Congress has until Sept. 30 to pass government funding legislation and avoid its third shutdown of the year. Republicans are particularly eager to avoid a shutdown roughly a month before a midterm election when they're trying to hold onto their congressional majorities.

Shelby added on Monday that while wall funding and border security are "important," senators were going to focus on keeping the government open.