Republicans have objected to initiating bicameral negotiations to resolve the differences between the two chambers' budgets until Democrats agree to rule out new taxes and a debt ceiling increase in the final report. Democrats say those decisions should be made in the negotiations.
McCain called the GOP's stance "a little bit bizarre."
Sen. Susan Collins (R-ME) sided with McCain, calling it a "entirely reasonable" to begin conference negotiations and hold a vote in both chambers on the final product.
"We have called repeatedly for a return to regular order in this body. Well, regular order is going to conference," Collins said. She said her party's stance "certainly is ironic at the least. It is an opportunity for the Republican House to argue for its budget."
Paul objected to going to conference, claiming that Democrats want to use the budget negotiations to "orchestrate a back-room deal to raise the debt ceiling."
He was joined by Cruz, who insisted the debt ceiling should not be raised absent major spending cuts -- and should thus be subject to a supermajority-threshold for passage. If the House and Senate negotiators agreed on a unified budget, including a debt ceiling increase, it would be immune from filibuster.
Senate Budget Chair Patty Murray (D-WA) reminded Cruz that Republicans will have an opportunity to vote on the final product and called on them to let the process play out.
Senate Minority Leader Mitch McConnell (R-KY) and House Speaker John Boehner (R-OH) also object to beginning conference negotiations on the budget.