Senate Democrats are celebrating a hard-fought win on Tuesday after passing a $95 billion aid package for Ukraine, Israel and Taiwan that President Biden had requested for months, but House GOP leaders are signaling that the victory could be short-lived.

"Right now, the Senate is the birthplace of poor policy. The lack of serious border security measures in this foreign aid package shows how disconnected this bill is from reality," Republican Policy Committee Chairman Gary Palmer, R-Ala., the No. 5 House Republican, told Fox News Digital. 

"The Senate has ignored the House of Representatives and the will of the American people this entire Congress. The American people… want the southern border secure."

Majority Whip Tom Emmer, R-Minn., meanwhile, warned that the House would not simply "rubber stamp" whatever Senate Majority Leader Chuck Schumer, D-N.Y., presented and said any aid package "must secure our own borders" as well.

"Americans elected our majority with a mandate to get Biden’s border crisis under control, and we will not abandon that directive to rubber stamp a foreign aid package that the Schumer Senate rammed through overnight," Emmer told Fox News Digital.

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Twenty-two Senate Republicans joined all but three leftist lawmakers to pass the supplemental aid bill after debating it through the night. But even before it passed early on Tuesday morning, Speaker Mike Johnson, R-La., signaled it may not even get a vote in his chamber.

"The mandate of national security supplemental legislation was to secure America’s own border before sending additional foreign aid around the world. It is what the American people demand and deserve," Johnson said in a Monday night statement. "Now, in the absence of having received any single border policy change from the Senate, the House will have to continue to work its own will on these important matters."

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A source close to Johnson confirmed to Fox News Digital the speaker does not intend to put the package up for a vote in the House, at least "not in its current form."

Meanwhile, the GOP senators leading opposition to the bill already began re-calibrating their focus on pressuring the House not to act even before it passed the Senate.

Sen. Ron Johnson, R-Wis., spoke on X Spaces on Monday evening with X owner Elon Musk, former 2024 presidential candidate Vivek Ramaswamy, and fellow supplemental aid critic Sen. JD Vance, R-Ohio, where Johnson conceded the package was likely to pass.

"We can get to the House, get them to stop this," he added.

Rep. Chip Roy, R-Texas, responded to Johnson’s statement on the bill with his own brief reaction, "This is good. We gotta hold the line."

The Senate bill came together quickly after an earlier version, a $118 billion aid package that also included border and immigration reforms, fell apart despite months of sensitive bipartisan negotiations. 

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Republicans in the House and Senate had closed ranks and demanded the Biden administration do something about the border crisis before they could support aid to Ukraine, which has become an increasingly polarizing issue within the GOP.

But key Republican leaders lambasted the deal soon after it came out, claiming it did not go far enough to stop the flow of migrants at the U.S.-Mexico border. Johnson led House Republicans in insisting that only an executive order by President Biden could fix the crisis.

Rep. Jim Himes, D-Conn., the top Democrat on the House Intelligence Committee, urged Johnson to let the House vote on the Senate’s bill in his own statement Tuesday. He also accused Republicans of kowtowing to former President Donald Trump, who had publicly urged them to oppose the Senate’s bipartisan deal.

"The House may never consider this critical bill because Speaker Johnson and other Republicans, many of whom claim to support our allies, live in fear of Donald Trump and his MAGA acolytes, a group that openly celebrates Putin and roots for Russia," Himes said.

"Speaker Johnson, I was with you in the White House, one day after taking the gavel, when you said we would pass an aid package for our allies. If your words mean anything, let the House vote."