She added that bills under suspension are usually reserved for naming post offices or congratulating winning sports teams.

"To give a constitutional amendment the same consideration as renaming a post office is embarrassing for us and a disgrace to the dignity and tradition of the House," she said.

The bill would cut $917 billion over 10 years, require Congress to find another $1.8 trillion by the end of this year, and require a balanced-budget amendment vote under a suspension of the rules. Earlier in the day, House Republicans decided to hold a vote on two possible amendments in an attempt to win support from Democrats.

Slaughter warned Democrats against agreeing to the GOP bill because it calls for cuts but does not say what might get cut. Other Democrats criticized the process as well.

"I keep expecting lion tamers and acrobats to appear on the House floor, because this process under this Republican leadership has become a complete circus," said Rep. Jim McGovern (D-Mass.). "Their approach is reckless, their approach is wrong, their approach is unfair, and I urge my colleagues to vote against this rule and against this bill."

Rep. Ed MarkeyEdward (Ed) John MarkeyMarkey fundraises ahead of Kennedy primary challenge The Hill's Campaign Report: De Blasio drops out | Warren gains support from black voters | Sanders retools campaign team | Warning signs for Tillis in NC Sanders defends job losses from ending use of fossil fuels MORE (D-Mass.) charged that Republicans want to keep the budget crisis going until the next election. "If America goes into default, it will be your fault," Markey said.

He also said the GOP was being driving by the Tea Party. "This Republican default will impose a Tea Party tax on the entire country," he said. "The Tea Party has congressional Republicans wrapped around its little finger, but it's the American people who are going to get squeezed."

And Rep. Debbie Wasserman Schultz (D-Fla.) reiterated Democratic arguments that tax hikes need to be a part of the answer.

"On a day when ExxonMobil's second quarter profits soared 41 percent and they earned $10 billion, it is simply unconscionable for us to ask seniors, working families, children and middle-class folks to bear the burden of our deficits when we are asking nothing -- nothing -- of corporations, special interests and the wealthiest few," she said.

Republicans defended their plan, in part by saying President Obama has no plan at all that can even be compared to the GOP bill.

"There's nothing," said Rep. Jack Kingston (R-Ga.). "Nothing but silence."

The House began debating the rule for the House bill just before 1 p.m.

-- This story was updated at 1:23 p.m.