Democrats have argued more specifically that the House budget plan would end the Medicare guarantee, as it would provide payment support for seniors to buy private health insurance in about a decade.

Rep. Tom Reed (R-N.Y.) argued briefly that Democrats were not raising a substantive point of order that might prevent consideration of the bill. He also spent some time rebutting Democratic charges that Republicans are looking to end Medicare.

"It does not end Medicare as we know it," Reed said. "It does not throw seniors off the cliff."

Republicans have said they need to deem passage of their budget — even though it has not been approved by the Senate — in order to start considering appropriations bills this year.

After the Democratic objection, the House voted 234-183 to proceed to debate on the rule.

—This story was updated at 1:16 p.m.