TIME's Jeffrey Birnbaum and Michael Duffy report that seven centrist politicians have been quietly plotting a run for the White House. In two late October conference calls, the schemers concluded that there is a hunger for a party that is fiscally conservative, socially liberal, pro-environment and in favor of campaign-finance reform. Next Sunday, the group members, which include Democratic Senator Bill Bradley of New Jersey, former Republican Senator and Independent Governor of Connecticut Lowell Weicker and former Democratic Senators Paul Tsongas of Massachusetts and Gary Hart of Colorado, will hold their most important call yet. They will decide whether one of them will run as an independent to challenge the two-party system. Bradley would be the most likely choice, but a recent campaign-style swing through California caused barely a ripple. Tsongas, Hart and Weicker have all shown a reluctance to run, and the other three group members -- former Colorado GovernorDick Lamm, former Minnesota Rep. Tim Penny (a budget-cutting Democrat) and the current Governor of Maine, Angus King, an Independent -- are barely known outside their states. Even if the group is unable to field its own candidate, it would like to nudge those in the race toward their positions. "They would like to run somebody," says Birnbaum, "but more importantly, this is in response to polls that show there is a huge interest by a large segment of the population in an alternative to the Republican and Democratic Parties."