“I have tremendous respect for this institution,” Mr. Rubio said in an interview on Friday. “But I’m not all that interested in the way things have always been done around here.”…

But the budget hawks have not budged, and they have even taken aim at their party in strikingly critical language.

“Here is the dirty little secret about some of those on the right side of the aisle,” Mr. Cruz said of his fellow Republicans. “There are some who would very much like to cast a symbolic vote against raising the debt ceiling and nonetheless allow our friends on the left side of the aisle to raise the debt ceiling. That, to some Republicans, is the ideal outcome.”

Mr. McCain called the demands of his Republican colleagues “absolutely out of line and unprecedented.” The Senate passed the budget before dawn on March 23 after a grueling all-night session, he noted, saying it was time to try to reach a final deal with the House in a negotiating conference.