Majority Leader Mitch McConnell said lawmakers will finish their work this week.
The presidential candidate said millions could lose their insurance over the GOP bill.
Democrats remained mum about what other changes they might offer.
The votes come amid the climate talks in Paris.
Julian Hattem 12/01/15 04:19 PM EST
The bill comes a day after the White House challenged Congress to act.
Cruz's comments are worthy of "five Pinocchios," Sen. Dick Durbin said.
The Republican leader says the details of bill are still being worked out.
Three people died during last week's shooting at a facility in Colorado Springs.
Supporters increasingly view the omnibus spending package as their best vehicle.
Julian Hattem 12/01/15 01:53 PM EST
A compromise bill outlining policy for the nation's spy agencies passed in a voice vote.