The impact of such efforts is dubious, however, and could help the incumbents, many of whom represent conservative Southern districts.
One exception is the Arkansas Senate race, where liberals are putting cash and muscle behind a bid to unseat conservative Democratic Sen. Blanche Lincoln, who had a mixed record on the health care bill. At least three unions have pledged $1 million each to a challenge by Arkansas Lt. Gov. Bill Halter in the state's May 18 primary. MoveOn.org has chipped in $1.6 million more and counting.
The anti-incumbent campaign is the follow-through on threats from liberal groups who played a pivotal role in helping Democrats win Congress and the White House in the last two elections. Over the past year, as Democratic leaders struggled to round up reluctant lawmakers to pass the health care bill, the groups warned the party's conservatives that a "no" vote would be viewed as political treason, with Election Day consequences.
"We made it very clear to all members of Congress that working families needed and expected their vote," said Lori Lodes, spokeswoman for the Service Employees International Union. "A lot of these members had campaigned on improving health care. They had made promises ... and voting against health care was just not acceptable."
"There has to be a certain level of accountability," she added.
Finding the right levers of accountability has been difficult, in part because the party establishment wants no part in the effort, making clear that it is more concerned about maintaining majorities than punishing its own.
In North Carolina, where liberals were furious with Democratic Reps. Mike McIntyre, Heath Shuler and Larry Kissell for opposing the bill, the SEIU is trying to launch a new party called North Carolina First. But the campaign hasn't identified candidates yet, and it has collected fewer than a third of the 85,000 signatures required by June 1 to get its candidates on the ballot.
In New York, the labor-backed Working Families Party is exploring challenges against Reps. Michael Arcuri and Michael McMahon, but again the movement has yet to name viable contenders.
Elsewhere, the groups have even less clout, in part because there is little appetite for liberal causes in many of the districts. Lodes, with SEIU, acknowledged that it isn't going after Democrats in the Deep South because it has few or no union members there.
In some cases, getting criticized by unions or liberal activist groups is good politics for a conservative Democrat. In others, losing campaign contributions could really hurt.
Underscoring their limited options, liberal leaders acknowledge that their efforts could ultimately help Republicans win tight races instead of getting more congressional representation to their liking.
Ilyse Hogue, MoveOn.org's director of political advocacy and communications, said Democrats have built big enough margins that "we don't need an extra 20 votes if they're going to be 'no' votes." The Democrats who voted against health care won't get "a dime of support or an hour of our volunteers' time," she said.
"This is a fight for the soul of the Democratic Party," she said. "Will we take some losses? I hope not, but maybe if that's what's required to remind people of the priorities that Democrats should stand for."
The GOP needs to reclaim 40 House seats in November to win the House, and 10 to take the Senate. Many political experts are predicting significant Democratic losses and possibly a Republican takeover of the House.
Establishment Democrats -- both liberal and conservative -- say it's misguided in that kind of environment for unions or others to launch even symbolic campaigns against incumbent Democrats.
Rep. Gerry Connolly of Virginia, who is among many vulnerable Democrats in the South, voted for the health care bill after some hesitation. He said he understands the passion on the left, but "I'm not sure how producing a House Speaker John Boehner and Majority Leader Eric Canter furthers the goals of MoveOn.org," he said, referring to the top Republicans who could take over leadership jobs if the GOP wins control of the House.
Retiring Democrat Bart Gordon of Tennessee called the labor efforts counterproductive.
"They may not agree with them on every vote, but I don't agree with my wife on everything either," he said.