“I’m just kind of fed up,” said Senator Lisa Murkowski of Alaska, a moderate Republican who has increasingly become a key vote for Democratic legislation. “He’s a leader. Why is he not leading this Senate? Why is he choosing to ignore the fact that he has a minority party that he needs to work with, that actually has some decent ideas? Why is he bringing down the institution of the Senate?”

Mr. Reid’s brutish style matters beyond the marbled chamber of the Senate. Senate legislation has increasingly turned into a battle over amendments and Mr. Reid’s uncompromising control over the process. The six Republicans who voted to take up the unemployment bill on Tuesday expected at least to be allowed votes on their amendments to shape the legislation.

Instead, Mr. Reid dismissed all Republican proposals as unacceptable and then proposed his own new unemployment deal. Under it, benefits would be extended until mid-November of this year, and paid for largely by extending a 2 percent cut to Medicare health providers in 2024. Republicans were outraged, and an obscure procedural fight is likely to leave up to three million out-of-work Americans without benefits.

“We need to be able to have votes on behalf of our states,” said Senator Kelly Ayotte, Republican of New Hampshire, who was denied a vote on her amendment to pay for the extension by requiring applicants for the child tax credit to have Social Security numbers, a proposal Mr. Reid declared an attack on children. “I don’t know what the issue is, unless you are afraid it will pass.”

Ms. Murkowski said that she was unlikely to support the bill.

The unemployment bill is only the most recent example of legislation that has become stuck in a procedural quagmire, affecting senators in both parties. A long-awaited showdown between two Democratic senators, Kirsten E. Gillibrand of New York and Claire McCaskill of Missouri, over the military’s approach to sexual assault fizzled late last year when they were denied any votes on an annual military policy bill that usually is shaped over weeks on the Senate floor. A bipartisan bill on Iran sanctions has yet to receive floor consideration. And Democrats, eager to replace a tax on medical devices that helps pay for the Affordable Care Act, have been denied a vote.