Sen. Claire McCaskill said a recent report about contracts is raising questions.
The Senate voted 70-27 in favor of a policy bill, defying Obama's veto threat.
“I can’t imagine a more callous, heartless remark," Rep. Blumenauer said.
Democrats cited McCarthy's controversial comments last week.
Julian Hattem 10/07/15 12:30 PM EDT
Rep. Louise Slaughter is moving ahead with a privileged resolution.
Rep. Walter Jones is calling for leadership candidates with "misdeeds" to drop out.
Sen. David Vitter's bill will head directly to the Senate floor.
Rep. Alan Grayson says the committee was designed to harm Hillary Clinton.
The Nevada Democrat said he would speak out until Republicans shut down the committee.
The Senate will take a final vote on the National Defense Authorization Act (NDAA).