Senator Mitch McConnell, the longtime Republican leader, has been outspoken over the past year about challenging the isolationist wing of his party that was questioning continued aid to Ukraine. He put his influence and reputation on the line to make the case that it was in the United States’ interest to help a beleaguered democracy trying to beat a Russian invasion led by Vladimir V. Putin, and expressed confidence that his party would join him.

But the Kentucky Republican’s optimism turned out to be misplaced. Mr. McConnell, who traveled to Kyiv last year in a show of continued U.S. support for the war effort, is now leading a filibuster against a bill to fund it, and is on the cusp of seeing the opportunity for more aid slip away entirely.

The increasingly bitter stalemate will be extremely difficult to resolve before funding runs out despite months of intense efforts by Mr. McConnell, the minority leader, to sustain it.

It is the latest indication of the waning influence of the minority leader, and how his party — once defined by an interventionist view that the United States should use its power to bolster democracies around the world — has shifted under his feet.

Mr. McConnell has regularly beat the drum to rally congressional backing for Ukraine with near-daily floor speeches and rounds of media interviews. In addition to his visit to Kyiv last May, he recently brought the Ukrainian ambassador to his hometown, Louisville.

Yet Republican politics have changed, leaving Mr. McConnell out of step with many of his colleagues and wearing away his powers of persuasion on an issue he has characterized as the paramount foreign policy question of the moment. Opposition to funding the war in Ukraine has become a political rallying point for the hard right, and Republicans in Congress are increasingly turning against it, in line with what polls show is a drop in public support.