The decision by Republicans in Congress to torpedo a bipartisan border deal they demanded has left the fate of aid to Ukraine and Israel in peril, closing off what had been seen as the best remaining avenue on Capitol Hill for approval of critical military aid to American allies.

The political paralysis in the face of pleas from President Biden, lawmakers in both parties and leaders around the world for quick action raised immediate questions about whether Congress would be able to salvage the emergency aid package — and if so, how.

In the Republican-led House, where many conservatives have resisted new aid to Kyiv and the border deal negotiated in the Senate, lawmakers were set on Tuesday to vote on legislation sending $17.6 billion in military assistance to Israel. But that measure was facing steep resistance from hard-right Republicans who complained that the money was not paired with spending cuts, as well as Democrats and Mr. Biden, who has threatened a veto, calling the bill a cynical attempt to pre-empt the security legislation brokered in the Senate.

The $118.3 billion Senate bill, which is set for a test vote on Wednesday, also appeared to be dead even before it reached the floor, after an increasing number of Republicans — even those who led the charge to negotiate it — declared they would vote to block it.

“Joe Biden will never enforce any new law and refuses to use the tools he already has today to end this crisis,” Senator John Barrasso of Wyoming, the No. 3 Republican, said. “I cannot vote for this bill. Americans will turn to the upcoming election to end the border crisis.”

The grim reality appeared to be sinking in for the nation’s allies and diplomatic leaders who for months have anxiously watched and hoped for momentum on Capitol Hill for approving aid, despite clear signs that the strong bipartisan consensus for such a measure was fraying.

In an unusual letter, a group of U.S. ambassadors stationed in the Indo-Pacific region had urged congressional leaders on Monday to secure passage of legislation providing assistance to Ukraine, Israel and allies in the Pacific, saying America’s credibility with its strategic partners is on the line.

But what Mr. Biden and others had hoped might be a temporary political problem standing in the way of such an effort instead appeared to be a fundamental change in the dynamic in Congress that could doom it completely.

For months, many in the White House and abroad had followed conventional wisdom and assumed that the combined will of a handful of like-minded congressional leaders, national security committee chairs and Mr. Biden would be enough to push new funding to Ukraine across the finish line.

But a restive G.O.P. voter base is dead set against sending another round of aid to Ukraine, and rank-and-file Republicans, especially in the slim-majority House, have flexed their muscles to oppose any real movement.

After reports indicated there was no clear path ahead for Congress to approve aid to Ukraine and Israel on Tuesday morning, Representative Matt Gaetz of Florida was exultant on social media. He cited a line from the film “Apocalypse Now”: “I love the smell of napalm in the morning!”