President Biden’s sweeping emergency spending measure to fund the war in Ukraine teetered on the brink of collapse in Congress on Wednesday as Republicans prepared to block it in the Senate over their demands to attach unrelated measures cracking down on migration into the United States.

With a critical late afternoon vote looming, Mr. Biden and Democrats on Capitol Hill pleaded in increasingly urgent terms for Republicans to drop their opposition and allow the $111 billion spending bill to move forward. They warned that a refusal to do so would be a historic failure that would play into the hands of President Vladimir V. Putin of Russia. The measure would speed about $50 billion in security assistance to Ukraine and another $14 billion to Israel, as well as money to counter threats in the Indo-Pacific region and to fortify the U.S.-Mexico border.

The money for Ukraine, which would also receive a fresh infusion of economic and humanitarian assistance, was by far the most substantial element of the legislation. It was also the biggest point of contention as Republicans in Congress have increasingly turned against funding the war effort there.

“Make no mistake: Today’s vote is going to be long remembered, and history is going to judge harshly those who turned their backs on freedom’s cause,” Mr. Biden said at the White House. He said Republicans were “willing to literally kneecap Ukraine on the battlefield and damage our national security in the process.”

Mr. Biden said he was calling on Congress to “do the right thing,” adding: “Stand against the tyranny of Putin. Stand for freedom.”

But Republicans, even those who have been ardent supporters of continued American backing for Ukraine’s war effort, appeared unmoved and unwilling to drop their insistence on major immigration policy changes as the price of more help for Kyiv.