“We’ve got the hall,” he said of the chamber. “We’ve got the people,” he said of his colleagues. “We just can’t get them to debate,” he said of the Democrats. “I’m just sort of at a loss.”
Democrats said that Republicans led by Senator Mitch McConnell of Kentucky were determined to lure them into votes on issues beyond efforts to protect 700,000 undocumented immigrants brought into the United States as children — the “Dreamers” who are the top priority for Democrats.
Mr. McConnell’s first offer was to call a vote on a Republican plan to punish so-called sanctuary cities — jurisdictions where local agencies do not cooperate with federal immigration officials in rounding up undocumented immigrants. That issue could be a political problem for those Democrats up for re-election in conservative states.
Senator Chuck Schumer of New York, the Democratic leader, blocked that effort, saying Mr. McConnell was starting off on the wrong foot.
“The majority leader’s desire to vote on an unrelated, partisan immigration bill — legislation that is not only silent on Dreamers, but is silent on border security as well — is not a productive way to begin debate,” Mr. Schumer said.
Mr. Schumer, instead, wanted to begin with a vote on President Trump’s conservative immigration plan — one likely to fail because of the absence of bipartisan support in an outcome meant to embarrass the president and show that his proposal cannot become law, building momentum for an alternative. Republicans were not interested in the Democratic maneuver.
“It is the prerogative of the majority to set the agenda,” Mr. Cornyn said.
The standoff has left the Senate right where it has been for years — frozen by a deep reluctance on the part of leaders of both parties to force vulnerable incumbents to take politically challenging votes. That thinking has dried up floor debate and put tight restrictions on the movement of legislation, making it a central cause of congressional gridlock.
In 2014, Republicans could not get enough of pointing out that Senator Mark Begich, a first-term Democrat from Alaska, never had a single amendment he wrote voted on by the Senate, a fact they said highlighted a lack of influence. He lost his re-election bid.
The refusal to battle it out over amendments has frustrated lawmakers in both parties and left some strategists scratching their heads because they see little evidence that such votes are all that damaging in an environment where charges and countercharges fly freely.
“What I came here to do is vote,” said Senator Richard Blumenthal, Democrat of Connecticut. “And I am chagrined that we are in a time when both sides seem in trepidation of voting because our political process has become so polarized.”
This fight was supposed to be different. After provoking a brief government shutdown last month, Democrats agreed to support the necessary spending to reopen federal agencies in exchange for a promise from Mr. McConnell that he would allow a no-holds-barred debate on immigration policy. It fell short of the demand by Democrats for a solution to the Dreamer issue but offered the party hope that, because of bipartisan sympathy for the immigrants, it could push through a bill and pressure the House to pass it.
But while Mr. McConnell might have promised the debate, he did not promise to make it easy for Democrats. As could have readily been predicted, he is getting behind the most conservative option presented on behalf of the president while trying to ensnare Democrats in tough votes to help preserve his majority in November’s elections.
“My Democratic colleagues have spent months demanding the Senate take up this issue,” Mr. McConnell said Wednesday. “They even shut down the government — unnecessarily, I might add — in order to secure this very week of debate. But now that the time has come to make law instead of just making points, they’re stalling.”
Democrats and a handful of Republicans that day were coalescing behind a compromise plan that would protect Dreamers but prevent parents who brought them into the country from gaining citizenship while diverting $25 billion to border security. Mr. McConnell also took steps to finally force action on a few amendments, but it was far from certain that any measure could gain the needed 60 votes.
What was certain was that the debate many anticipated was not going to occur in a Senate that hosted storied fights between John C. Calhoun and Daniel Webster over slavery. Stephen A. Douglas and Abraham Lincoln later clashed in a series of remarkable showdowns as they sought the Senate seat from Illinois in 1858, setting Mr. Lincoln up for his presidential election despite his Senate loss.
And in October 2008, Senator Joseph R. Biden Jr. of Delaware and Gov. Sarah Palin of Alaska squared off for the right to preside over the Senate as vice president of the United States. “Can I call you Joe?” Ms. Palin asked in a more memorable moment.
The confrontation this week was shaping up as a test of whether the Senate could regain its debate footing. So far, the institution is failing.