At a briefing with reporters at the Capitol, Hoyer said that the House could pass fixes to the Senate's healthcare bill before approving it. The measure is unpopular in the House.

Under this process, the House would pass a package of fixes to the healthcare bill, which would then move to the Senate, where they would be considered under budget reconciliation rules requiring only a majority vote.

After that, Hoyer said, the House could pass the Senate bill. The president would then sign the underlying bill first and the fixes second.

Hoyer admitted the alternative option is "more complicated," but said that it is possible.

Most of the focus in Washignton has been on a plan in which the House would pass the Senate bill first. The corrections package would then go through the House and the Senate.

Hoyer did not give an indication as to which path forward is preferred by members of Congress or the House or Senate leadership.

House leaders have not yet said whether they have the votes to proceed with the Senate bill first, however, and Republicans doubt they do. Approving the fixes first could be a way to win additional votes for the Senate bill in the House.

The alternative proposal would allow House lawmakers who have balked at supporting the Senate bill because of certain provisions, such as the so-called "Cornhusker kickback," to vote for a bill removing those provisions before voting for one with them included. 

Hoyer said this weekend that the House must act first to finalize healthcare reform, but did not go into depth about what piece of legislation, the main bill or the fixes, would pass first.

President Barack ObamaBarack ObamaOvernight Tech: FCC chief gives states more control over internet subsidies | Dems urge Trump to veto bill blocking online privacy rules | House boosts its mobile security Overnight Defense: Pentagon considers more troops for Afghanistan | McCain, Graham won't back short-term funding | GOP defends Trump rules of engagement Paul Ryan sells out conservatives with healthcare surrender MORE is expected to unveil his path forward on healthcare reform, but the details of his proposal are still unclear. 

Hoyer said earlier on Tuesday that reports that the president will press Congress to pass a smaller health bill are not true.