Speaker Mike Johnson is pushing House Republicans to enact President Trump's policies through the reconciliation process. (Getty Images)
A senior House GOP aide said it was "extremely unlikely" for the resolution to pass through committee this week.
Meanwhile, the national debt continues to climb past the $36 trillion mark, with the U.S. deficit currently running over $710 billion for this fiscal year.
House Republicans huddled at Trump National Doral golf course and resort for three days last week, where committee chairs detailed possible avenues to pursue spending cuts.
Senate and House Republicans hope to use their majorities to pass a broad range of Trump’s agenda items through reconciliation. By lowering the threshold for Senate passage from 60 votes to 51, it will allow Republicans to bypass Democrats and enact sweeping policy changes – provided they are linked to the budget and other fiscal matters.
But to do that, the House Budget Committee will need to pass a budget resolution that will include specific instructions for various other committees under policies of their jurisdiction.
Conservatives have demanded that the final product of the process be deficit-neutral, if not deficit-reducing – something Johnson promised last week.
Rep. Ralph Norman said he wanted to see at least $1.3 trillion more in spending cuts than GOP leaders' latest offer. (Chip Somodevilla/Getty Images)
But steeper spending cuts could also risk rankling Republicans in districts that depend on whatever funding goes on the chopping block.
Democrats have used Republicans’ pursuit of deep spending cuts as a cudgel, accusing them of wanting to gut Social Security and Medicare. GOP leaders have denied eyeing those benefits.
Rep. Ben Cline, R-Va., another Freedom Caucus member on the budget panel, said he was optimistic but that there were "a lot of conversations about starting the process from the most conservative position possible."
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"The Senate is not as interested in fiscal responsibility, so we recognize the need to set parameters for authorizing committees that encourage that… from the beginning," Cline said.
Johnson said he wanted the bill through committee this week for a goal of passing an initial House version by the end of February.
Congressional leaders hope to have passed a reconciliation bill by May.
The speaker said on "Fox & Friends" Monday morning of reconciliation talks, "Republicans are working right now to negotiate what that looks like. We don't want to blow a hole in the deficit by extending the Trump-era tax cuts, for example, but we're definitely going to get that extended. So we got to find those savings."
Elizabeth Elkind is a politics reporter for Fox News Digital leading coverage of the House of Representatives. Previous digital bylines seen at Daily Mail and CBS News.
Follow on Twitter at @liz_elkind and send tips to elizabeth.elkind@fox.com
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