The Senate FInance Committee should be able to craft a bipartisan healthcare bill, as long as they're not "overruled" or "undercut" by President Obama and Senate Majority Leader Harry ReidHarry ReidTop Lobbyists 2017: Grass roots Boehner confronted Reid after criticism from Senate floor GOP in uncharted territory rolling back rules through resolutions MORE (D-Nev.), Sen. Chuck GrassleyCharles (Chuck) Ernest GrassleySenators push mandatory sexual harassment training for members, staff Senate panel to hold hearing on bump stocks, background checks Senate panel to hold hearing on bump stocks MORE (R-Iowa) said Thursday.

Grassley told Iowa reporters during a regular press call that he believes Senate Democrats could probably pass a bill using budget reconciliation rules requiring only a simple majority vote, but that bipartisanship could succeed if given time.

Finance Committee Chairman Max BaucusMax Sieben BaucusTop Lobbyists 2017: Hired Guns GOP tries to keep spotlight on taxes amid Mueller charges Clinton-Sanders tensions linger for Democrats MORE (D-Mont.) will be able to eventually reach a bipartisan agreement on a healthcare bill "if he doesn't get overruled by the leader or the president," argued Grassley, the ranking member of that committee.

"Sen. Baucus has always been talking about 70 or 80 votes," Grassley later added. "We're still going down that direction, but we could be undercut by anybody."

Both Baucus and Grassley have worked throughout August with the so-called "group of six" centrist senators on healthcare reform, though Baucus -- backed up by Senate Democratic leaders -- has imposed a September 15th deadline by which a bipartisan bill must be reached.

After then, Democrats have left the door open to using the budget reconciliation process to pass a preliminary healthcare bill, which may be a version including a public (or "government-run") option as written by the Senate Health, Education, Labor, and Pensions (HELP) committee.

Grassley said he believed Democrats could be able to pass a bill in that circumstance, but not any one he or any other Republican would support.

"I think the Democrats could pass one under a process called reconciliation," he said. "If they do that, one would pass for sure without any Republican support whatsoever, and I couldn't vote for it."