And although Democrats could use a procedural rule they passed earlier this year to push through some healthcare legislation with a simple majority, the rule may prevent them from enacting a comprehensive bill.
Baucus and Grassley have been among the fiercest critics of a single-party approach.
"Fundamentally, legislation that is historic, that is comprehensive, that has a large number of senators supporting it is more durable," Baucus said in an interview. "It will be more sustainable and will inspire more public confidence."
Baucus, who came to the Senate in 1979, and Grassley, who joined two years later, have let that philosophy guide them since they assumed senior posts on the finance committee eight years ago.
The two do not socialize outside of the Senate. But since 2001, they have met nearly every Tuesday at 5 p.m. in Baucus' conference room on the fifth floor of the Hart Senate Office Building. (The coffee is free there, the parsimonious Grassley likes to joke.)
Both men said that they slowly grew to trust one another and to look for places where they could agree.
"We are pragmatists," Grassley said while in Iowa recently to meet with constituents. "We come from similar states, and I think we have a similar idea of what bipartisanship is all about."
Said Baucus: "Most people in this country want us to basically work together, to get something done between the 20-yard lines. They are in the center."
Their bipartisanship has at times grated on their colleagues, however.
Baucus infuriated fellow Democrats by working for President George W. Bush's tax cuts in 2001 and then featuring a photo of himself with Bush in a campaign flier during his 2002 reelection campaign.
It was only last year that Baucus emerged as a leading champion of universal healthcare, a goal that Democrats have been chasing since the Great Depression.
From the start, he enlisted Grassley's help.
The two senators' staffs have been in almost daily contact, hashing out language for a bill that Baucus has promised will expand coverage, hold down costs and improve quality.
Whereas Democrats on Kennedy's health committee developed their bill largely by themselves and then showed it to their GOP colleagues -- a process that infuriated Republicans -- aides to Baucus and Grassley "started with a blank sheet of paper," as one Republican staffer said.