Washington - The Senate moved closer Tuesday to a deal to avert a partial shutdown of the Department of Homeland Security, but the proposal faced an uncertain future in the House, where Republican leaders conspicuously refused to embrace it.

Senate Majority Leader Mitch McConnell, R-Ky., told reporters he was prepared to move swiftly on a bill to extend funding for DHS through the fiscal year that is not contingent on Republican demands to repeal President Barack Obama's executive actions on immigration.

Under McConnell's proposal, the Senate would vote first on the funding measure and then hold a separate vote on a bill to undo the Obama's new immigration initiatives. McConnell hopes to assuage conservatives who are determined to confront the president on what they see as abuse of his executive authority.

"I don't know what's not to like about this," McConnell said. "This is an approach that respects both points of view." If successful, the proposal would break a two-month deadlock over funding for the agency that is responsible for border security , airport security checks and a range of other functions.

But House Speaker John Boehner, R-Ohio, did not immediately warm to the proposal and it was not clear whether he could marshal enough backing in his chamber to complete the deal to keep DHS open beyond Friday, when its spending authority expires.

House Republicans will huddle behind closed doors this morning. The unsettled DHS debate is expected to be the central focus of their discussion.

The stalemate between Republicans in the House and the Senate has tested the new Republican majority's ability to govern. Senate Democrats have blocked four attempts by McConnell to move forward on a House bill that would fund the department, but which ties that funding to repeal of the president's immigration orders, which allow millions of undocumented immigrants temprorary reprieve from deportation.

McConnell's move represented a concession in a fight that has threatened what would be a second partial government shutdown in less than two years. In October 2013, a broad swath of the federal government was shuttered for more than two weeks over a fierce budget fight between Republicans and Democrats.

Senate Minority Leader Harry Reid, D-Nev., said Democrats want assurances from Boehner that a "clean" funding bill will pass the House before they would support McConnell's plan and allow the votes to move forward.

"Now, all eyes are on Speaker Boehner," Sen. Charles Schumer, D-N.Y., said.

Asked about the emerging Senate plan, Boehner spokesman Michael Steel said in an email: "The Speaker has been clear: the House has acted, and now Senate Democrats need to stop hiding. Will they continue to block funding for the Department of Homeland Security or not?"

Exiting a House leadership meeting later on, House Rules Committee Chairman Pete Sessions, R-Texas, said he did not support approving McConnell's plan. Instead, Sessions said Congress should pass a temporary extension of funding for up to six weeks and convene a House-Senate conference to try to hammer out the differences between the two chambers.

DHS is scheduled to begin furloughing nonessential workers if Congress does not extend its $40 billion budget by Friday.

At the White House, Obama prepared to inject himself more forcefully into the debate with a town hall-style forum planned today in Miami, which has a heavily Latino population. The president is expected to address both the funding standoff his immigration plan. The administration has appealed a federal judge's decision last week temporarily blocking the deferred deportations program under which up to 5 million of the nation's 11 million undocumented immigrants would be eligible for renewable, three-year deportation waivers and many could receive work permits.

As the president rallies the public, however, Obama and his aides have limited their dealings with Capitol Hill. White House and Democratic aides said that there is little the president can do because he will not undo his immigration actions. It is up to Republicans to decide whether they are willing to shut down DHS over the issue, the aides said.

"This is not a battle with the White House. This is a battle taking place on Capitol Hill," a White House official said, speaking on the condition of anonymity to discuss internal thinking. "Legislators on the Hill need to work on this. . . . What you're going to see from the administration on DHS up until Friday is continuing to call attention publicly to the potential impact of shutting down DHS."

To that end, Homeland Security Secretary Jeh Johnson and two predecessors from the George W. Bush administration - Michael Chertoff and Tom Ridge - will attend a news conference scheduled for today to warn of problems that could occur if the agency is forced to begin furloughs.

Essential personnel, as many as 200,000 employees, would continue to report to work without pay during a partial shutdown. Although Johnson and the White House have said that national security would not be jeopardized, they have warned that long-term planning could be affected. In an interview, Chertoff warned of morale problems in the agency and said he thinks a shutdown would "no doubt adversely affect the nation's security."

"A couple days of delay (of pay) will not make a difference, but if it starts to mount up and there's real uncertainty, people will start to feel demoralized, and that could have an impact over a long period," Chertoff said. "You wouldn't do this to (military) troops in the field, send them into combat but not get paid. They need to take this seriously."

While McConnell's plan to split off the immigration issue into a standalone measure opened the door to winning over Democrats, conservatives were skeptical.

"Senators arguing fund DHS but vote a separate bill to defund executive amnesty. Have you heard of Obama veto? Think we were born yesterday?" Rep. Steve King, R-Iowa, a staunch opponent of Obama's immigration actions, wrote on Twitter.

Meanwhile, the administration has struggled to explain how a partial shutdown would affect national security. White House press secretary Josh Earnest, asked repeatedly about it Monday, declined to say whether the nation would be more at risk. Rather, he said the situation would not improve the nation's safety.

"It's hard to imagine a good time for Congress to be mucking around with the funding of the Department of Homeland Security," Earnest said. "But now seems like a particularly bad one."

Politically, the standoff could help the White House and Democrats. Republicans drew the brunt of public anger over the 2013 shutdown and administration aides believe the same would happen if DHS is affected at week's end.

It is not lost on White House allies that the president is traveling to Florida, a key swing state in presidential races, to hold his rally today.

"In our travels to the immigrant community, the faith community, the law enforcement community and the business community, they want someone in D.C. to do something," said Ali Noorani, executive director of the National Immigration Forum. "The president has done something. The political risk to the administration is only there if they stop doing something. Right now, it's on Republicans to kind of meet the bar."

Senior administration officials are scheduled to appear at another immigration forum, hosted by Univision, on Sunday in Los Angeles, which has the largest number of immigrants potentially eligible for deportation relief under Obama's executive actions.

"For the first time in a long time the immigrant community and advocates are very aligned with the White House," said Marielena Hincapié, executive director of the National Immigration Law Center. "I think the fact that he's coming to Miami to meet with immigrant community members and take questions directly from folks speaks volumes."