To rein in costs, the GOP plan converts Medicare to a type of voucher system for those currently under 55. Instead of government-run Medicare, seniors would buy private insurance and the government would foot some of the bill.

Rehberg added, "There are just too many unanswered questions as to exactly how it will work."

Budget Committee Chairman Paul RyanPaul Davis RyanRepublicans are avoiding gun talks as election looms The Hill's 12:30 Report Flake to try to force vote on DACA stopgap plan MORE (R-Wis.) proposed a budget that seeks to drastically limit government spending, including $5.8 trillion in cuts over the next decade.

Freshman Rep. David McKinleyDavid Bennett McKinleySenators offer bill to close rural-urban internet divide Lawmakers battle Trump, PhRMA on discount drug rule House rejects Democrat's resolution to impeach Trump MORE (R-W.Va.) also voted against the measure, which is expected to stall in the Democratically controlled Senate.

He too cited cuts to Medicare as the reason for his vote.

"My home state of West Virginia has the highest percentage of Medicare beneficiaries in the country, and I cannot support a plan that the Congressional Budget Office (CBO) has determined would nearly double out-of-pocket healthcare costs for future retirees," he said in a statement.

McKinley, who announced on Thursday that he'd raised $536,654 in the first three months of 2011, represents the district formerly held by Democratic Rep. Alan Mollohan for more than two decades. He won election last November by less than 1 percent of the vote.

Reps. Walter Jones (N.C.) and Ron Paul (Texas), both in safe districts, were the other Republicans who voted against the resolution.

— Erik Wasson and Pete Kasperowicz contributed to this report.

— This post was updated at 7:54 p.m. on April 16