House Majority Leader Kevin McCarthy, R-Calif., said Wednesday that it's "possible" the House would take up legislation tomorrow to partially repeal and replace Obamacare, but said no formal plans have been made yet.

"Members should be prepared to be here and voting tomorrow," he said on the House floor when answering questions about Thursday's schedule.

McCarthy was pressed repeatedly by House Minority Leader Steny Hoyer, D-Md., about whether the bill would come up tomorrow or later in the week.

In reply, McCarthy said only that Republicans had made "significant" progress on the bill.

"When we are ready to bring the bill to the floor, I will make an announcement and relay scheduling information to all members," he said.

There has been talk of voting Thursday or even later this week on the amended bill, which gives states the flexibility to opt out of Obamacare mandates, and also includes new language to help states pay for high medical costs.