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.
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.
The Nevada Democrat tied the leaks to a "political hit job" against Clinton.
The Republican says Obama will have to decide whether to veto the legislation.
The vote comes as the administration and lawmakers grapple with the Syrian humanitarian crisis.
But the Arkansas senator is keeping his block on one ambassador nomination.