A split of Mike Johnson, left, and Donald Trump. (Getty Images)
The House's version, which the chamber passed in late February, calls for at least $1.5 to $2 trillion in federal spending cuts to offset the new spending for Trump's priorities on defense, the border and taxes.
The Senate passed an amendment to the House version over the weekend that, while closely mirroring the lower chamber, called for at least $4 billion in spending cuts.
Sources told Fox News Digital that there are as many as 30 to 40 people who have at least shared serious concerns about the bill.
Some skeptics are expected to be part of a group of House Republicans heading to the White House on Tuesday afternoon to meet with Trump.
But at least three lawmakers who have shared concerns about the bill – Reps. Tim Burchett, R-Tenn., Ralph Norman, R-S.C., and Keith Self, R-Texas – said they were not invited.
SENATE GOP PUSHES TRUMP BUDGET FRAMEWORK THROUGH AFTER MARATHON VOTE SERIES
Meanwhile, House Freedom Caucus Chairman Andy Harris, R-Md., signaled to reporters that he turned the invitation down.
"There's nothing I don't understand about this issue. So, you know, let the president spend time with people who maybe will change their mind," Harris said.
He said of Trump's influence, "It’s not going to help getting enough votes to pass this week. It's just, there too many members who are just not going to vote for it, no matter what."
Senate Majority Leader John Thune speaks during a news conference following the Senate Republican policy luncheon at the US Capitol. (Al Drago/Bloomberg via Getty Images)
"The budget resolution is not the law, OK? All this does is it allows us to continue the process, begin drafting the actual legislation that really counts. And that's the one big, beautiful bill. Number two, the Senate amendment makes no changes to the reconciliation instructions that we put into the budget resolution. So our objectives remain intact," Speaker Mike Johnson, R-La., said during his weekly press conference.
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"Number three, any final reconciliation bill has to include historic spending reductions that we included in our, resolution while also safeguarding essential programs."
But fiscal hawks critical of the bill, like Harris, are pushing Republican leaders to allow the House to begin working on its reconciliation bill now and forcing the Senate to reckon with that proposal.
And some Republican holdouts are optimistic that Trump could get them to a point where they can support the legislation Wednesday.
"I sure hope he can," Norman told Fox News Digital. "We're in favor of what he's doing."
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
https://www.foxnews.com/politics/house-republicans-worry-even-trump-cant-save-them-tax-cuts-budget-bill-hang-balance