Cooler heads prevailed on the Senate floor Thursday night after Oklahoma Republican Sen. Tom Coburn initially threatened to stall completion of the annual defense authorization bill amidst a feud with New York Democratic Sen. Charles E. Schumer about a gun rights amendment.

Senate Armed Services Chairman Carl Levin, D-Mich., offered an agreement to set up consideration of a set of amendments, including a Coburn proposal to make it more difficult to keep veterans from owning guns. Schumer objected when he learned the amendment was in the queue.

“We have senators objecting to protecting the rights of the people who defend us,” Coburn said.

Coburn initially said he would block any other requests, grabbing the attention of senators and staffers still in the Capitol late Thursday. But he relented after some prodding from Sen. John McCain, ranking member on the Armed Services panel. The Arizona senator cautioned fellow Republicans against moves that could delay the fiscal 2013 defense policy measure because doing so could give more fodder to Democrats supporting a standoff over the Senate’s rules.

“There’s more here, frankly, than just a refusal to allow an amendment,” McCain said. “That is going to mean that it’s more likely that we have this showdown, which we think — many of us think — would be devastating to this institution and the way that it’s done business for a couple of hundred years.”

Schumer, a gun control supporter and the No. 3 Democratic leader, has succeeded in keeping the Coburn proposal from a vote. He said, however, that his effort to keep the amendment from reaching the floor should not be equated with the tactics Coburn has deployed through the years.

“We’re in a little bit of Alice in Wonderland. The number of times that I have risen to my feet to object because I didn’t want an amendment to come forward can be counted on a single hand in this body over the last year or two,” Schumer said. “My good colleague from Oklahoma … he has made himself a legislative powerhouse, regularly using that practice.”

Schumer suggested Coburn got his amendment on the list by threatening to block or object to proposals from all other senators.

“It’s well-known that my good friend from Oklahoma and others have used the very rule that I have used tonight over and over and over again,” Schumer said.

Gun issues are always complicated for the Democratic caucus. Majority Leader Harry Reid hails from Nevada, very much a pro-gun-ownership state, while other members of his leadership team hail from states with major urban areas that favor restrictions on gun ownership.

It is the second time this week that the amendment has surfaced. Coburn’s office contended that Reid prevented it from coming up for a vote during debate on a sportsmen’s bill that could not overcome a budgetary hurdle this week.

Senators declined to waive a budgetary point of order against that bill (S 3525) in a 50-44 vote Monday.

The amendment would require a more formal legal review of cases regarding the mental health of veterans than currently required before keeping them from having firearms.

Lawmakers want to finish the defense bill (S 3254) by week’s end.

“All we’re asking for the veterans of this country is that if their rights are taken away, that it be adjudicated by a judge or a magistrate,” Coburn said.