House Republican leaders will offer a series of bills to replace Obamacare in an effort to bring in enough GOP support to pass separate legislation to repeal and replace the healthcare law.

House Ways and Means Committee Chairman Kevin Brady told reporters early Tuesday that he would soon advance a measure to tighten up who is eligible for healthcare subsidies.

The measure was proposed by Rep. Lou Barletta, R-Pa., who, as a result of Brady's commitment to move his bill, has switched from a "no" to a "yes" on the repeal-and-replace measure.

The bill would be debated and voted on separately from the repeal-and-replace measure, and would likely be among several other separate bills aimed at bringing reluctant Republicans who believe the repeal-and-replace measure falls short in some areas.

The provisions can't be added to the repeal-and-replace measure, however, because they would run afoul of Senate rules governing how the legislation can be passed in that chamber.

"We have several continued improvements to the replacement that would go separately this month," Brady told reporters before entering a closed-door GOP meeting in the Capitol basement.

Sources tell the Washington Examiner the GOP is about a half dozen votes short of the 216 majority needed to pass the repeal-and-replace bill.

Time is running out to move that measure. The House is scheduled to leave for a week-long recess on Thursday and has only until late May to use a budgetary rule that would allow the repeal and replacement of Obamacare to move through the Senate with just 51 votes.

Brady said he would advance Barletta's proposal in the tax-writing committee by the end of May.

"Right now we have several [bills] that could move with that as well," Brady said.

Barletta has argued that the repeal-and-replace measure on its own does not adequately prevent illegal immigrants from receiving heath insurance tax credits.