, Mark Pynes , Associated Press
House Speaker John Boehner, left, and Senate Majority Leader Mitch McConnell meet with the press at the GOP retreat at the Hershey Lodge in Hershey, Pa., Thursday, Jan. 15, 2015.

HERSHEY, Pa. — Not exactly brimming with confidence, Majority Leader Mitch McConnell says he's going to try to push a House-passed bill to overturn President Barack Obama's immigration policies through the Senate.

But neither McConnell nor other members of his leadership — and not even senior House Republicans — predict success for the plan that undoes Obama's moves and exposes hundreds of thousands of younger immigrants to deportation.

"Good question," Sen. John Thune, R-S.D., said Thursday when asked about the bill's prospects in the Senate. "It's a process," added Rep. Cathy McMorris Rodgers, R-Wash., equally noncommittal on the subject as Republicans held a joint retreat in this capital of chocolates and sweets.

The $39.7 billion legislation funds the Homeland Security Department for the remainder of the budget year while undoing executive actions by Obama offering protections to millions of immigrants in the country illegally.

"We're going to try to pass it. That'll be our first choice," McConnell told reporters at a news conference at the homey Hershey Lodge. "If we're unable to do that, we'll let you know what comes next."

Although the Senate is now under GOP control, Republicans are still six votes shy of the 60-vote margin needed to advance most legislation. But Democrats aren't McConnell's only problem. A number of Senate Republicans have concerns with the House approach, which used the Homeland Security spending bill for priorities like cybersecurity and counterterrorism as the vehicle to take a stand against Obama. In the wake of the Paris terror attacks, lawmakers don't want that legislation jeopardized.

"It's very difficult to craft language in a way that takes aim at the overreach by the president with his executive authority and yet doesn't impede DHS's enforcement of the law," said Sen. Susan Collins, R-Maine.

Funding for the Homeland Security Department expires at the end of February, so Republicans have until then to resolve the issue.

In addition to taking aim at Obama's executive actions on immigration from November, which extended protections to millions of immigrants here illegally who have kids who are citizens or residents, the House legislation would end a 2012 Obama program designed to give protections to young people. Some of the more centrist Republican lawmakers are opposed to it for that reason.

The legislation also faces an Obama veto threat.

Republican leaders renewed pledges Thursday not to let funding for the Homeland Security Department expire, or risk a government shutdown.

"I anticipate we'll act well in advance of that. There aren't going to be any more — no more drama associated with shutting down, for example, the Department of Homeland Security. That's off the table," said Sen. John Cornyn, R-Texas.

Even Republicans who support the House-passed bill expect to end up approving something that falls short of it. But what, exactly, still must be determined once lawmakers return to Washington and their Capitol offices.

"I know what we got done and that was absolutely the high-water mark. Everyone knows that, but I'm not ready to say we'll end up with nothing," said Rep. Steve Stivers, R-Ohio.