The former Illinois lawmaker said BoehnerJohn Andrew BoehnerA warning to Ryan’s successor: The Speakership is no cakewalk With Ryan out, let’s blow up the process for selecting the next Speaker Race for Republican Speaker rare chance to unify party for election MORE risked allowing Democrats in the minority — and the White House — to drive House votes by not insisting on majority Republican support.

"When you start passing stuff that your members are not in line with, all of a sudden, your ability to lead is in jeopardy because somebody else is making decisions," Hastert said. "The president is making decisions, [House Minority Leader Nancy] Pelosi [(D-Calif.)] is making decisions, or they are making the decisions in the Senate."

Hastert also warned that Boehner risked abdicating the House's traditional and constitutional authority to dictate spending bills with the deal, which was negotiated primarily in the Senate.

"All tax bills and all spending bills under the Constitution start in the house, when you give up that responsibility you really give up your responsibility to govern, and that is the problem," Hastert said.

Hastert had previously said that on some issues, he could see allowing a Speaker violating his namesake rule, although again cautioned against doing so.

"On occasion, a particular issue might excite a majority made up mostly of the minority," Hastert told the Washington Post in 2004. "Campaign finance is a particularly good example of this phenomenon. The job of speaker is not to expedite legislation that runs counter to the wishes of the majority of his majority."