She said Maine’s experience with insurance exchanges to create more flexibility for consumers had persuaded her that for less-populated states, the exchanges had to extend beyond state borders. She also thinks the idea of a reinsurance program to have the federal government absorb the risks of some catastrophic health care costs in an effort to lower private premiums is worth exploring.

All of this means that Ms. Snowe, a senior member of the Finance Committee with a longtime interest in health policy, is the chief Democratic target. And with Senator Edward M. Kennedy’s death leaving Democrats a single vote shy of the 60 required to overcome Republican procedural objections at least temporarily, their need to entice at least one Republican to cross the aisle has become more critical.

Image Senator Charles E. Grassley of Iowa. Credit... Susan Walsh/Associated Press

It is hardly the first time Democrats have turned to Ms. Snowe for help.

Most recently, she was one of three Republicans to back President Obama’s economic stimulus plan, pushing that legislation over the top and frustrating her Republican colleagues.

Along with Senator Susan Collins, her fellow Maine Republican, Ms. Snowe has backed Democratic budget plans opposed by most of her party. She has balked at some tax cuts, pushed for more attention to rising federal deficits and generally shown a willingness to split from Republicans on issues where she sees more common ground with Democrats.

“She has courage, real courage,” said Senator Kent Conrad of North Dakota, one of the Finance Committee Democrats in the Group of Six who, as chairman of the Budget Committee, has also worked with Ms. Snowe on fiscal issues.

Rahm Emanuel, the White House chief of staff, who has consulted with Ms. Snowe, said: “She is really in it for the policy. When you think of an ideal senator, regardless of party or philosophy, Olympia Snowe really fits that mold.”