A loose governing coalition appears to be emerging, with roughly a third of the Senate’s Republicans joining nearly every Democrat in various deals to avert the “nuclear option” and pass the immigration overhaul — and, down the line, potentially avert a budget crisis.

“I think you’re going to find bipartisan groups doing many different things, more than before,” Sen. Charles E. Schumer, D-N.Y., told reporters Wednesday following the rollout of a new gang pushing media shield legislation.

“In the Senate, you have to work in a bipartisan way,” Schumer said. “We are legislators. We like to legislate, and it’s not very satisfying to just go to the floor and make a speech knowing that it won’t have any result in making the country a better place.”

Schumer’s been in the middle of two of the biggest bipartisan deals in recent months. He was a member of the “gang of eight” that drafted the Senate’s immigration overhaul, and more recently he worked with some of the same senators (and a few newcomers) on the deal to get a number of executive branch nominees lined up for confirmation without deploying the nuclear option to change precedents with a simple majority vote to curb filibusters.

On both occasions, Schumer worked with Arizona Republican Sen. John McCain. Schumer said Tuesday that the pair talked some 30 times over the weekend on the filibuster deal. On Wednesday, Schumer said he’d broached with McCain the idea of working on the next big-ticket item: the budget debate that looms after the August recess.

“I think he would desire — I’ve talked to him a little bit about it, of trying to again avoid a standoff and coming to some kind of agreement,” Schumer said. “He’s somebody who has the respect of his colleagues on both sides of the aisle and would rather get something done than just stand and point.”

For his part, McCain said he could envision a scenario where many of the same senators involved in the nuclear option talks reappear if there’s a budget showdown approaching at the end of the fiscal year on Sept. 30.

McCain cited Republican Sens. Bob Corker and Lamar Alexander of Tennessee, John Hoeven of North Dakota, Susan Collins of Maine and South Carolina’s Lindsey Graham “of course” as part of the most recent working group, noting that he was probably leaving out someone important. He said it wasn’t much of a gang because there was such a tight deadline and most of the business was conducted by telephone.

“It was a very short-lived gang,” McCain said, before concurring with the suggestion that another emergency group could appear to help prevent another budget debacle. “Oh yeah, I could, because there are people here who are result-oriented that — who their colleagues trust.”

Hoeven emerged as a deal-maker on the immigration bill, teaming up with Corker on the border surge amendment that helped the “gang of eight” get an overwhelming Senate vote. He said Wednesday that the debt limit and appropriations debates might be more difficult, but need to be solved.

“The short answer is, I hope so,” Hoeven said of getting a bipartisan group going.

“We’re going to face this debt limit, debt ceiling issue pretty soon. Obviously we have reduced the deficit, but there’s a lot more to do,” Hoeven said. “It’s going to take bipartisanship to come up with the real solutions. I mean, obviously that’s what we have to do is we’ve got to find ways to come together to address the challenges for the American people.”

A core of Republicans largely in McCain’s orbit have spearheaded the new emerging wing of the GOP interested more in governing than in grandstanding. But the group of lawmakers has shifted a bit with each vote — 17 Republicans voted to end the filibuster of Consumer Financial Protection Bureau head Richard Cordray, 14 voted for the immigration overhaul, and just five (Alexander, Collins, Corker, Mark S. Kirk of Illinois and Lisa Murkowski of Alaska) joined McCain in backing cloture on Thomas E. Perez as Labor secretary on Wednesday.

The next big test will likely come in appropriations, where the parties remain far apart on whether the topline number should be set at levels assuming the sequester remains in place. Senate appropriators have regularly reported bills to the floor, but Senate Majority Leader Harry Reid, D-Nev., has yet to bring any of them to the floor for a test of how that process may work.

That could well change before the August recess, with a Democratic aide saying Reid could put the Transportation-HUD spending measure on the floor in the coming weeks.

“We have a real sticking point,” on spending bills, the aide said. “Even though we’re appropriating and going through and doing the … committee work and subcommittee work, it’s going to be a real challenge when it gets to the floor because we’ve got to balance to the [budget] number. That’s the law.”

Of course, while a number of Senate Republicans, including McCain, have spoken in favor of going to a House-Senate conference committee on the fiscal 2014 budget resolution, another GOP block has prevented repeated efforts by Budget Chairwoman Patty Murray of Washington and other Democrats to do that.