Instead of threatening a new party, they could support the Greens. The full article mentions the Working Families party as well.
Politico: Liberals warn Democrats on health care
Labor and progressive leaders are threatening House Democrats who oppose health care legislation with potentially destructive third party challenges in November.
In districts where Democrats vote “no,” voters “will have the Republican against health and the Democrat against health care, and they’re going to ask themselves, ‘Where’s the candidate that shares my values,’” [SEIU President]Stern told POLITICO. “A lot of us would like to run another candidate.”
“I am not the only labor leader looking at [the question of] what is the price of betrayal,” he said, suggesting that Pennsylvania and Illinois could also see liberal third party challenges.
The left has already sponsored a serious primary challenge to Senator Blanche Lincoln in Arkansas, but backing third-party candidates – who could easily split the vote and hand a seat to the Republicans – would mark a new level of disgust with Democrats opposed to health care.
Rules for independent candidacies vary by state, and New York’s labor-backed Working Families Party has already taken the first step, with its state committee voting to bar endorsements of any candidate who votes against health care legislation.