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House Republicans are leaning towards a strategy to voice disapproval of the president’s immigration executive action while keeping most of the federal government funded through September 2015.

A proposal discussed behind closed doors Tuesday would include a House vote this week on a bill or resolution expressing opposition to the president’s new policy to offer deportation relief and work permits to millions of undocumented immigrants. Then, the House would vote next week on a package of 11 bills to keep the government funded for nearly a year – meeting the December 11 deadline to keep the government’s doors open without an unpopular federal shutdown.

But one agency would not be fully funded: the Department of Homeland Security, which will lead implementation of Obama’s executive action. The department would only be funded at current levels until March, giving Republicans further leverage in the spring – when they control both houses of Congress – to try to defund the new policies.

The complicated two-step comes as some Republicans on House Speaker John Boehner’s right flank want to use the threat of a government shutdown to force Obama’s hand on immigration.

Boehner said Tuesday that, while he views Obama’s executive action as “a serious threat to our system of government,” Congress has few ways to strike at the heart of the policy it opposes.

“Frankly, we have limited options and limited abilities to deal with it directly,” he said.

Furthermore, Senate Minority Leader Mitch McConnell – who will soon be elevated to Majority Leader – has been adamant that a government shutdown will not occur on his watch.

Early signs showed that the floated two-pronged approach has some traction with the conservative House Republicans who most insist on immediate action to counter the president’s immigration order.

"If they are determined to go forward and honor the work of the Appropriations Committee, fine, carry that out until the end of September,” said Iowa Rep. Steve King, a leader of Republicans opposed to comprehensive immigration reform. “I think it would be better not to but I am not going to oppose that."

The disapproval resolution is almost certain to go nowhere in the short term; while Democrats control the Senate for the remainder of the year, Senate Majority Leader Harry Reid is sure to ignore it.

The short-term funding of the Department of Homeland Security is also likely to draw opposition. In a hearing before the House Homeland Security Committee Tuesday, DHS chief Jeh Johnson said that such piecemeal funding would prevent him from hiring new Secret Service agents, maintaining detention facilities in Texas or build upon border security efforts.

NBC's Shaquille Brewster contributed to this report.