Senate Democrats picked up some GOP reinforcements in their bid to get to a conference on a House-Senate budget agreement.

Republican Sens. John McCain of Arizona and Susan Collins of Maine joined Budget Chairwoman Patty Murray, D-Wash., on the floor in support of going to conference without imposing special mandates on conferees.

McCain objected to a bid by Sen. Rand Paul, R-Ky., to require that Senate budget negotiators not provide for an increase in the debt limit. Instead, McCain called for a more established process of offering nonbinding instructions.

“That’s the way we should do business in the United States Senate. … Now, the senator from Washington may not like those instructions, but the fact is that those are the way we do business, not require the conferees to take certain measures,” McCain said.

Paul said Democrats are “trying to orchestrate a back-room deal to raise the debt ceiling.”

“Raising the debt ceiling is an incredibly important debate. Shouldn’t be done in a back-room debate, shouldn’t be done by a few people, shouldn’t be done through parliamentary trickery or chicanery,” Paul said. “It should be done full out in the open, under the ordinary rules of the Senate.”

Over the past few weeks, Democrats have been repeatedly pressuring Republicans to allow them to send the budget to conference, but they have been consistently blocked by a handful of Senate conservatives.

Allowing a debt limit increase through budget reconciliation would require agreement from House GOP budget conferees, which would be led by Rep. Paul D. Ryan, R-Wis. McCain highlighted that point during a floor exchange with Collins.

“Isn’t that a little bit bizarre?” McCain asked Collins.

“It certainly is ironic at the least. It is an opportunity for the Republican House to argue for its budget,” Collins responded. “I voted against the final version of the Senate budget, but I think we should go to conference and try to work out an agreement.”

Majority Leader Harry Reid, D-Nev., chimed in after McCain and Collins.

“We’ve just heard something here somewhat unusual,” Reid said. “It’s kinda old-fashioned, but it’s called regular order. What they’re saying we should do is go to conference, and we have had in years past lots of motions to instruct. That’s … the way we used to do things around here … and to get off base on a debt ceiling matter has nothing to do with what we’re doing.”

“There’s simply no reason why the very reasonable approach suggested by Sen. McCain that would allow us to go to conference should not be adopted,” Collins said. “We have called repeatedly for a return to regular order in this body. Well, regular order is going to conference.”

“It’s important that there be a conference committee to work out the differences, which are considerable, so that we will have a framework with binding allocations for the Appropriations Committee,” said Collins, a member of the spending panel.

Paul was joined by Republican Sens. Ted Cruz of Texas and Mike Lee of Utah in supporting the requirement that a budget conference not include tax hikes or debt limit increases. Cruz and Paul said that this was exactly the right time to debate the debt ceiling, concerned another chance might not present itself.