"Every member of this House has a victory in the bill", said Rep. Tom Cole, R-Okla. "We need to make sure that the people who are supposed to represent us, people who are meeting about this right now in Washington, understand that very clearly". The money in Upton's plan would go to people in states that get those waivers.
A major blow came when Republican moderate Rep. Fred Upton of MI announced he'd vote against it out of concern it doesn't do enough to cover patients with pre-existing conditions.
In a phone call, the two leaders talked about how to reduce the suffering in Syria, including the possibility of safe zones, according to a White House summary. An amendment that would let states waive some of those requirements has garnered the votes of reluctant conservatives but left more moderate Republicans concerned. Mulvaney argued that Trump's victory was in avoiding a politically-embarrassing shutdown that could play into the hands of White House opponents and critics.
Trump could, if he wanted, refuse to sign the bill funding the government up to September, which is still being finalized in Congress.
House Speaker Paul Ryan told Republicans Tuesday to "pray" as they try to win over the remaining holdouts on the health-care bill with leaders pushing for a vote later this week.
They're insisting that it represents a win for the administration.
The Trump administration also came out in support of the measure on Tuesday. He was joined at his second briefing by Homeland Security Secretary John Kelly.
That contradicted Trump's message of less than a week ago.
"When you heard in the last 48 hours about the deal, did you think we could build this?"
The budget is funded through Saturday, and the bill being considered in the House would extend it through September.
Democrats touted the lack of funding for the border wall. When asked why the administration requested money at all, if indeed Mexico was going to pay for it, Mulvaney said the answer was simple.
Trump had complained earlier Tuesday about having to work with Democrats, tweeting that, "Our country needs a good "shutdown" in September to fix mess!"
Trump's congressional allies have cut a deal with Democrats to fund the government until September. The truth of the matter though is now we've averted a government shutdown in a way that allows the president to fund his priorities, " Mulvaney said.
The Republican health care bill has been dealt a significant blow with a respected former House committee chairman saying he doesn't support it. He said the measure would undermine insurance protections current law gives people with pre-existing illnesses, which legislation supporters disputed. The other blocks insurers from charging different rates to healthy and sick customers.
Upton's defection could make it easier for other moderates to vote no.
Including Upton, The Associated Press has counted 21 GOP lawmakers opposing the Republican bill, one shy of the 22 needed to kill it, assuming all Democrats vote no. "We don't have the votes but we're nearly there".
Congress is expected to vote on the five-month spending bill before midnight Friday, the deadline to prevent a partial shutdown.
Trump planned to discuss the health care bill with four key House members, including Reps.
In March, the CBO, a bipartisan research office, forecast that the first Republican-backed healthcare bill would cause 14 million Americans to lose their insurance by next year and 24 million more than now would be without coverage by 2026.