Senate Republicans want a 60-vote threshold for a debt-limit bill to pass the chamber, but it’s actually Democrats who are enforcing the filibuster on their own legislation, insisting on delaying a vote until 1 a.m. Sunday morning.

Republicans offered to let the vote happen Friday night, just minutes after the chamber voted to halt a House Republican bill. All sides expect Democrats’ bill will fail too, and the GOP said senators might as well kill both at the same time so that negotiations could move on to a compromise.

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“We would be happy to have that vote tonight,” Sen. Mitch McConnell, Republicans’ leader, offered.

But Senate Majority Leader Harry Reid objected, even though the vote would occur on his own bill. He instead said the chamber would have to run out the full procedural clock, which means a vote in the early hours Sunday morning.

He said he would be willing to move up the vote if Republicans didn’t insist on a 60-vote threshold, which has become traditional for big, controversial items to pass the Senate. But the GOP held firm on that demand, so Mr. Reid said he would insist on the full process, which he said would show the country that Republicans were being obstructionist.

“There is now another filibuster. That’s what this is. It’s a filibuster to stop us from moving forward,” he said.

Mr. Reid complained that if the House had been held to the same super majority rules the Senate often operates under, Republicans’ proposal never would have passed over there earlier in the day.

Under the rules, to end a filibuster usually requires a vote be delayed until two days after the parliamentary motion is made. But the Senate this year has repeatedly set 60-vote thresholds and held the votes without the two-day delay.

For their part, Democrats pointed to reports back in April that showed Republicans themselves were thinking about not insisting on the 60-vote threshold. Those plans were scuttled when it became clear some in the GOP wanted to scrape for every inch in the fight.

In lieu of a Senate vote, House Republicans themselves will introduce and then vote to kill the Reid plan on Saturday afternoon as a way to try to force negotiations into the next phase.