In the House, lawmakers like Mr. Kratovil, Mr. Cardoza and other swing Democrats will come under increasing scrutiny from leadership as a vote draws near. Of the 219 Democrats who initially voted in favor of the House measure, roughly 40 did so in part because it contained the so-called Stupak amendment, intended to discourage insurers from covering abortion.

Some, notably Representative Bart Stupak, the Michigan Democrat for whom the amendment is named, will almost certainly switch their yes votes to no because the new version being pushed by Mr. Obama would strip out the House bill’s abortion restrictions in favor of Senate language that many of them consider unacceptable.

An additional 39, like Mr. Kratovil, are fiscal conservatives who voted no the first time around. Ms. Pelosi is hoping that she can get some to switch those no votes to yes in favor of Mr. Obama’s less expensive measure.

Image Representative Bart Stupak, namesake of an amendment intended to limit abortion coverage. Credit... Sally Ryan for The New York Times

But persuading Democrats who are already on record as opposing a health overhaul to do a turnabout will not be an easy task, especially during a midterm election year in which Democrats’ political prospects already look bleak. Of the 39 Democrats who voted against the House measure, 31, including Mr. Kratovil, represent districts that were won in 2008 by Senator John McCain of Arizona, Mr. Obama’s Republican rival. Fourteen, including Mr. Kratovil, are freshmen, who are generally considered more politically vulnerable than more senior lawmakers.

“The concern among Democrats right now is that there are more yes votes reconsidering than no votes,” said David Wasserman, who tracks House races for the nonpartisan Cook Political Report. “My sense is that for Democrats to pass this bill, they would have to convince several members who are already in serious jeopardy, even after voting no on the first health care bill, to put passage of the bill ahead of their own chances of being competitive in the fall.”

But politicians do not want to be martyrs. They want to hold onto their seats.

Ms. Pelosi is facing resistance from some of her most senior members, like Representative Ike Skelton, Democrat of Missouri and chairman of the Armed Services Committee. He has been in office since 1977, but is facing his toughest re-election challenge in years.