Vice President Mike Pence warned Republicans in a closed-door meeting Tuesday not to oppose the GOP plan to repeal Obamacare, and said voting against it would be a vote in favor of Obamacare.

"If you like your Obamacare you can keep it," Pence told Republicans at a closed-door meeting Tuesday. "But the American people want change."

Pence was sent to Capitol Hill just hours after Republicans released their proposed bill, which drew immediate complaints from Republicans who are pushing for a full repeal of the law. Some called the GOP plan "Obamacare Lite."

Pence was peppered with questions by Republicans at the private meeting, and told reporters Trump is "determined to work with Congress" to repeal Obamacare and "replace it at the same time," with more affordable healthcare and more choices.

The White House on Tuesday cast the GOP bill as a "work in progress," a sign that changes may be necessary in order to move it through the House. Pence acknowledged that reality by saying as the legislative process goes forward, the GOP plan "is the framework for reform and we are certainly open to improvements and to recommendations in the legislative process."

But he also warned the GOP, "this is the bill" backed by President Trump.

In the meantime, Senate Republicans seem to be eagerly awaiting House passage of the bill. Senate Majority Leader Mitch McConnell indicated Tuesday he could decide to call up the House-passed bill for a vote, as he said lawmakers would have sufficient input as an Obamacare replacement measure churns through House committees beginning Wednesday.

Such a move by McConnell would skip over Senate committee consideration and make it more feasible for Republicans to meet a tight deadline to sent President Trump a bill to sign that both repeals Obamacare and partly replaces it.

A spokesman for McConnell said no decisions on process have been made. But McConnell told reporters after the GOP meeting with Pence that he is planning for the full Senate to vote on the measure before Congress adjourns for the two-week Easter recess on April 7.

"We are going to have plenty of time to look at it," McConnell, R-Ky., told reporters. "It is going to go through the regular order, the committee process in the House. There is going to be ample time to take a look at it and ample time to answer all the questions."

Senate Republican leaders believe they can pass the bill despite possible opposition from four Republican lawmakers who question the Medicaid reform provisions in the bill, and say they won't back a proposal that kicks people off the entitlement.

The GOP plan phases out the Medicaid expansion and turns it into a block grant system to reduce costs.

Other GOP lawmakers are unhappy with the House provision to provide tax credits, and are making the case they should be means tested, to prevent wealthier individuals from benefiting and to provide more for low-income earners.

Four Republicans on Monday warned in a letter that they would reject a bill that does not sufficiently protect the Medicaid expansion. It's not clear now whether the GOP proposal assuages their concerns.

"Everybody is trying to leverage their position and shape and influence the bill in the direction they want to see it," said Senate Republican Conference Committee Chairman John Thune, R-S.D.

Thune said he is pushing for means-tested tax credits and other changes he believes will help the measure "be strengthened and improved."

Thune said he believes Republican in the Senate will provide the 51 votes needed to pass the measure because it will be the only opportunity to end Obamacare and fulfill a years-long GOP pledge.

"When push comes to shove and there is a vote over here, it is going to either be a vote for the status quo or a vote to repeal this and move toward a better way," Thune said. "That is what members are going to be faced with and that is what is going to be the way I think it will be framed. It's going to be a yes or no vote."