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AGOA expires in September unless Congress acts, but Mr. Baucus said the uncertainty has already cost thousands of African women their jobs.

Democrats said Mr. Coburn himself had voted for the same budget technique repeatedly — something he acknowledged.

Indeed, Congress often tweaks the window on spending and taxes to make legislation fit within budget rules. Republicans did it with the 2003 tax cuts, while both parties have agreed to major deals in recent years that rely on the same technique.

For example, a bill in 2010 to extend full payments to doctors who treat Medicare patients for one year was paid for by halting overpayments of a tax credit in Democrats’ health law — even though the tax credit doesn’t kick in until 2014. In that instance, Congress reduced spending in the years 2014 through 2021 in order to pay for spending that was all paid out in 2011.

Mr. Coburn informed his colleagues earlier this week that he objected not only to the 10-year savings technique, but also another provision that restructures the way some corporations pay their tax liabilities, which he said in effect makes them overpay upfront.

It, too, has been used by Congress before — but Mr. Coburn said he’ll no longer accept it without a fight.

“I’m going to tell you, I’m not moving,” he said. “I’m not going to be a part of kicking the can down the road again.”

The Burma sanctions have been in place for years as the U.S. sought to bring pressure on a rogue regime.

But Myanmar recently has taken some strides toward democracy, including holding elections in which former dissident and Nobel Peace Prize winner Aung San Suu Kyi won a seat in parliament.

In the wake of those changes, the Obama administration sent an ambassador to the country and suspended some of the sanctions involving foreign investment. But other sanctions, such as a ban on military purchases from the U.S., remain in place.

Both the administration and members of Congress want the full sanctions law to remain in place as a prod to the country to continue its path.

Republicans tried to separate the two issues, offering to pass the Myanmar sanctions alone. Mr. Coburn even said he would accept a half-hour debate and a vote on an amendment to use a different funding stream — and said he expected to lose that vote.

But Democrats said if they gave him that vote, they would have to allow others to offer their amendments, and that would become too messy.

Sen. Mitch McConnell, the top Republican in the chamber and chief author of the sanctions, watched the fight in disbelief. He said he didn’t have a dog in the spending fight, but was shocked that Democrats would tie that to the sanctions.

“We have for the first time in the history of this issue turned it into a partisan matter,” he said.