A little-noticed Senate vote just before 4 in the morning on March 23 — amid the chamber’s 13-hour vote-a-rama on a fiscal 2014 budget resolution — suggests trouble for President Barack Obama’s gun control agenda.

Senators voted 50-49 in favor of an amendment by Sen. Mike Lee, R-Utah, to establish a two-thirds requirement for the passage of any gun control legislation in their chamber. While the budget resolution is nonbinding and the amendment did not win the 60 votes needed to be adopted, the outcome underscores how many senators strongly support gun rights, just as the chamber prepares to debate the biggest package of gun control measures in nearly two decades.

Six Democrats from gun-friendly states joined a nearly united Republican conference to support Lee’s amendment: Max Baucus of Montana, Joe Donnelly of Indiana, Kay Hagan of North Carolina, Heidi Heitkamp of North Dakota, Joe Manchin III of West Virginia and Mark Pryor of Arkansas.

All of those senators are being watched closely — and lobbied heavily — ahead of the Senate showdown on Obama’s gun measures when lawmakers return from their two-week recess in early April.

Only one Republican, Mark S. Kirk of Illinois, broke ranks with the GOP and voted against Lee’s amendment. Both independents, Angus King of Maine and Bernard Sanders of Vermont, also voted against it. Frank R. Lautenberg, a New Jersey Democrat and strong supporter of gun control legislation, missed the vote.

Lee’s amendment sought to require a 67-vote supermajority for Senate passage of all future restrictions on firearms and ammunition, and it used a broad definition of the term “gun control.” For example, beyond requiring the heightened vote threshold for a proposed ban on assault weapons and high-capacity magazines, the amendment also would have required it for any bill that “requires background checks through a federal firearms licensee for private transfer of firearms.”

The background check proposal is now the centerpiece of Obama’s push for tougher gun laws, and polls have shown it enjoys nearly 90-percent support among the public.

New York City Mayor Michael Bloomberg, a fierce advocate of more restrictive gun laws, announced over the weekend that he is funding a $12 million ad campaign in 13 states ahead of the Senate vote as a way to pressure senators to support the background check plan.

While it is unclear to what extent the early-morning vote on Lee’s amendment presages the outcome of the Senate’s coming debate on background checks and other gun provisions, gun-rights groups expressed optimism about their chances of defeating Obama’s proposals in the Senate. Meanwhile, there were other signs Monday that Bloomberg’s lobbying campaign may not change minds in the next two weeks, even for the senators who are being specifically targeted.

“I’ve gotten a lot of questions about NYC Mayor gun ad,” Pryor tweeted. “My response? I don’t take gun advice from the Mayor of NYC. I listen to Arkansans.”