A top House committee will advance a bill this week repealing parts of Obamacare using a special process that could send the bill to President Obama's desk.

The House Ways and Means Committee will mark up a bill Tuesday doing away with major sections of the Affordable Care Act through a process called budget reconciliation, which means Democrats wouldn't be able to filibuster it in the Senate.

Republicans have long debated using the reconciliation process, which would require Obama to veto the bill or agree to undermine his signature domestic reform. The president is likely to issue a veto, should the Senate send the legislation to him.

"The law is as unpopular as ever, and now is the time to use all the procedural tools at our disposal to directly challenge the president," the committee said Monday morning.

The House bill would do away with the law's individual mandate for Americans to buy health coverage, its employer mandate for companies to offer workers coverage and the Independent Medicare Payment Advisory Board, a panel designed to cut Medicare spending if it grows too fast.

The legislation also would ditch two of Obamacare's unpopular taxes: its levy on manufacturers of medical devices and its so-called "Cadillac tax" on high-cost health plans.

The full House plans to vote on the reconciliation bill after the committee passes it, but it's not clear whether the Senate will take up the bill after that. The House Education and the Workforce Committee also will consider a bill repealing part of Obamacare using reconciliation on Wednesday.