Sen. John Cornyn John CornynQuinnipiac polls show Trump leading Biden in Texas, deadlocked race in Ohio The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (R-Texas) said on Monday that he doesn’t support Ken Cuccinelli’s appointment as acting director of U.S. Citizenship and Immigration Services (USCIS) and that Cuccinelli likely wouldn’t be able to win confirmation for the role on a permanent basis.

“He’s made a career of attacking other Republicans and frankly attacking 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, so I doubt he’ll have the support to get confirmed,” Cornyn said.

Asked if he supported Cuccinelli atop the immigration agency, Cornyn said no.

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Cuccinelli began his new job as acting director of USCIS on Monday, a controversial move that came despite opposition among Senate Republicans to giving the former Senate Conservatives Fund leader a Senate-confirmed position.

The White House has not formally nominated him as director. He can remain in the acting position for 210 days.

Cuccinelli, however, could face a rocky road to confirmation should Trump nominate him to lead USCIS on a permanent basis.

Cuccinelli is replacing Lee Francis Cissna, who was forced out as USCIS chief late last month amid a shake-up at the department that was engineered by top White House policy adviser Stephen Miller Stephen MillerSpecial counsel investigating DeVos for potential Hatch Act violation: report Trump confirms another White House staffer tested positive for COVID-19 Biden pick creates furor, underscoring bitterness over Obama immigration policy MORE.

But Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) has long opposed the former Virginia attorney general, who worked in 2014 to oust McConnell.

"I've not spoken to him about any of them. I have expressed my, shall I say, lack of enthusiasm for one of them … Ken Cuccinelli," McConnell told reporters in April.

Republicans hold a 53-47 majority, meaning Cuccinelli would have to lose four GOP senators and win over no Democrats to not be confirmed.