Washington ( CNN ) -- House Republican leaders are aiming to delay a challenge to President Barack Obama 's controversial immigration executive order until early next year in an effort to avoid a government shutdown next week , multiple House GOP members and aides told CNN . Speaker John Boehner announced the strategy in a closed-door meeting of House Republicans Tuesday , where it was largely well-received by rank and file GOP members , although some conservatives are pressing for changes , according to multiple sources . Many members say they are still reviewing the details . At a news conference afterwards , Boehner said his members realize their hands are tied on the immigration issue until Republicans control both chambers of Congress in January . `` I think they understand that it 's going to be difficult to take meaningful action as long as we got Democrat control of the Senate , '' Boehner said . Mitch McConnell , the Kentucky Republican in line to become the next Senate majority leader , reiterated his view that the GOP should stop threatening shutdowns . `` We need to quit that kind of rattling the economy , '' McConnell said Tuesday at the Wall Street Journal CEO Council . The government will run out of money on Dec. 11 unless Congress acts . Last year 's government shutdown was politically disastrous for Republicans and the party is trying to avoid a repeat just as they 're on the cusp of retaking full control of Congress for the first time in nearly a decade . The GOP plan discussed on Tuesday calls for the House to vote on legislation that would fund most of the government through September while only funding the Department of Homeland Security , which would carry out key parts of the executive orders , until just sometime in March . That would give Republicans time to pass legislation blocking the immigration orders . House Republican leaders are trying to balance competing priorities in the party . They want to mollify conservatives who are furious over the President 's decision to make it easier for millions of undocumented immigrants to stay in the country by providing a clear opportunity for them to try to block the action . After hearing about the plan Tuesday morning , some of those House members on the right say they will oppose it because it would continue funding for agencies tasked with granting new visas through March of next year . `` You just want me to fund the unconstitutional act for 60 days ? Kind of like being a little bit pregnant ? It does n't work for me , '' Arizona GOP Rep Matt Salmon told reporters . But other Republicans -- including leaders in both chambers -- are fearful of tying that move to government funding . Arkansas GOP Rep. Steve Womack said now that voters gave his party control of both the House and Senate in the midterms it 's was important to demonstrate that they can govern and not `` give any opportunity for buyer 's remorse on the part of the discerning electorate . '' He said there was a `` narrow window '' for Republicans to show they can run the government before voters size up the parties again before the 2016 election . A vote on the bill is likely next week , aides said . Testifying before a House committee on Tuesday , Homeland Security Secretary Jeh Johnson urged lawmakers against legislation that would fund his department for a shorter period of time than the rest of the government . `` That is , in my judgment , a very bad idea for Homeland Security because during that period ... , we can not engage in new starts , '' Johnson said . `` For example , we are back in a presidential election cycle . I can not hire new Secret Service agents until I get an appropriations bill passed by this Congress -- not another ( continuing resolution ) for a couple of months . '' Senate Democrats generally support the President 's immigration orders and oppose the House plan to fund DHS just through March . But after meeting with his caucus Tuesday , Senate Democratic Leader Harry Reid it would be a `` big accomplishment '' if the House passed a bill that funded most of the government and signaled he would support it . Separately , the House likely will vote this week on a bill that essentially calls out Obama on immigration . House Judiciary Committee Chairman Robert Goodlatte is reworking a proposal drafted by Florida Republican Rep. Ted Yoho of Florida . That bill would allow members to `` vent '' about their unhappiness with the executive action and assert that what Obama did was unconstitutional . Illinois Republican Rep. Peter Roskam said the separate vote declaring the president violated the Constitution by using executive authority on immigration is to demonstrate to constituents that the GOP opposed the president 's actions . `` Silence is assent so to not respond in any way is in some fashion to be complicit in it , so this allows members to be on the record and clear about it . '' However , the bill would have not legal binding authority and the Senate is sure to ignore it . Salmon said he would vote for the bill because he opposed the president 's immigration actions , but then he essentially dismissed it , saying , `` it 's not going to go anywhere and everyone 's knows it . '' In addition to the funding strategy , House GOP members are also still considering whether they should sue the President for the issuing the directives that they consider unconstitutional . CNN 's Alexandra Jaffe and Jeremy Diamond contributed to this story .
NEW : Some are pressing for changes to GOP rules . Some are working on a plan that would avert a government shutdown . GOP could vote on the plan next week . Congress should act before Dec. 11 to avoid a shutdown .