Senate Republican Conference chair Lamar AlexanderAndrew (Lamar) Lamar AlexanderTrump to make ObamaCare payments to insurers for August CBO: ObamaCare premiums could rise 20 percent if Trump ends payments CBO to release report Tuesday on ending ObamaCare insurer payments MORE (R-Tenn.) said on Wednesday that healthcare reform legislation could pass through Congress "today."

"I think it's possible. I mean, [Obama] could pass a bill today," Lamar told Fox News' Trace Gallagher. The host asked Alexander if Congress could ratify the health bill by the end of the year.

"We'd like for him to start over and come up with something that we can join with him and support," he added.

The Tennessee Republican suggested the bipartisan Wyden-Bennett bill, which calls for private providers to serve as primary suppliers of universal coverage, as an alternative.

Alexander's remarks come at a time when healthcare reform faces obstacles in both the House and the Senate.

Senate Finance Committee chairman Max BaucusMax BaucusTrump has yet to travel west as president Healthcare profiles in courage and cowardice OPINION | On Trump-Russia probe, don’t underestimate Sen. Chuck Grassley MORE (D-Mont.) had set a September 15 deadline for his committee to present a bipartisan version of the legislation. Finance Committee Republicans and Democrats have been locked in intense negotiations over how to pay for the reforms.

Some Democratic senators have indicated they would move the bill through the upper chamber with a party line vote if delays continue. On the other hand, Senate Minority Whip Jon Kyl (R-Ariz.) predicted the deadline would pass without the Democrats forcing a party line vote.

On the other side of the Capitol, House Democratic leadership cut a deal with Blue Dog Democrats to move the bill through the Energy and Commerce Committee before they broke for recess last week. With three forms of the bill passed by different committees, the final form of the House legislation is still unknown.