Senate Majority Leader Mitch McConnell said Thursday he wants to move ahead with a vote on a recently-passed House bill to fund the Department of Homeland Security while also blocking some of President Obama’s key immigration policies.

However, there has been widespread speculation the bill will fail in the upper chamber because of the immigration amendments.

“My first choice is to try to pass the bill,” McConnell said at the GOP congressional policy retreat in Hershey, Pa.

The GOP-led House approved the legislation Wednesday, and if it passes, it also would overturn Obama’s key immigration policies and expose hundreds of thousands of younger immigrants to expulsion from the United States.

That was part of a broader bill that would provide $39.7 billion to finance the Homeland Security Department through the rest of the budget year.

Funding for the agency expires at the end of February.

“We’re passing a bill for political reasons, a bill that has no ability to pass the Senate,” California GOP Rep. Jeff Denham said after the House vote.

He was one of 26 House Republicans who voted against the legislation.

Even with Republicans in control of the Senate, the bill faces an uphill battle in the chamber, since backers are six votes shy of the 60-vote majority needed to advance most legislation.

Lawmakers of both parties said the legislation is sorely needed to pay for counterterrorism, cybersecurity and other priorities at a moment when the Paris terror attacks have underscored dire threats.

But Democrats accused Republicans of putting that money at risk by attaching veto-bait amendments on immigration, and some Republicans voiced the same concern.

In turn, GOP leaders and most of their rank and file accused Obama of reckless and unconstitutional actions on immigration that had to be answered.

Denham on Thursday said the House would not allow Homeland Security to run out money over the issue.

South Dakota GOP Sen. John Thune said the House bill coming to the Senate is “just the start of the process.”

FoxNews.com's Joseph Weber and The Associated Press contributed to this report.