Senate Majority Leader Harry Reid (D-Nev.) praised McCain as the key deal-maker in the matter.
But the longtime senator, who was his party's presidential nominee in 2008, was quick to say he wasn't usurping his party's leaders.
“I don't mean to replace the leadership — usurp it in anyway,” he said, adding “I'm just there to help.”
He said he talked to Senate Minority Leader Mitch McConnell (R-Ky.) several times over the weekend as he worked with Reid on negotiations.
“He was encouraging me. He wanted to get this done,” McCain said.
Sen. Lindsey Graham (R-S.C.), one of McCain's closest friends in the upper chamber, said the Arizona lawmaker was helping out because he “really loves the institution.”
“I think John looks long-term in terms of the Senate. I think he's trying to keep the Senate the way he found it,” Graham said.