With Senator Rand Paul’s decision to support a resolution to block President Trump’s emergency declaration, Congress appears ready to deliver a stern rebuke to the president over his border wall and a clear statement that it will defend its ability to control federal spending.

Senator Paul, a libertarian-minded Kentuckian, said he will join fellow Republican Senators Susan Collins of Maine, Lisa Murkowski of Alaska and Thom Tillis of North Carolina, giving proponents of the resolution of disapproval the 51 votes they need, if Democrats remain united in their support.

On Monday, Senator Mitch McConnell of Kentucky, the majority leader, confirmed that the measure has the votes to pass the Senate. Senate leadership, he said, has been conferring with the Senate parliamentarian to see if the House-passed resolution could be amended before the vote.

“It’s an interesting question,” Mr. McConnell said at a news conference in Kentucky. “It’s never been done before.”