With its attention primarily focused on Congress, MoveOn has yet to become vigorously involved in the 2008 presidential race, although its members have been encouraged at points to telephone Senators Hillary Rodham Clinton and Barack Obama’s offices to keep them in line on Iraq. Next week, it is beginning an advertising campaign against the Republican candidate Rudolph W. Giuliani in Iowa. Mr. Giuliani took out an advertisement yesterday in The Times attacking the group and Mrs. Clinton.

The group has held two online presidential forums, one on Iraq in April and the other on climate change in July. Mr. Obama, of Illinois, came out on top in a straw poll for offering the best hope for leading the country out of Iraq and John Edwards won on climate change.

Mrs. Clinton, of New York, trailed significantly in both.

“Anybody who has 3.2 million people in an organization and can mobilize and raise resources and things, they are going to have a big impact,” said Joe Trippi, a senior adviser to Mr. Edwards.

MoveOn has shown a willingness to depart from party orthodoxy on campaigns. Last year, despite party leaders’ entreaties, it took an active role in aiding the antiwar candidacy of Ned Lamont, who was trying to unseat Senator Joseph I. Lieberman of Connecticut, then a Democrat supporting the war effort.

Mr. Lamont won the Democratic primary. Mr. Lieberman ran as an independent in the general election and kept his seat.

“It’s good for the Democrats to have an engaged and vocal left,” said Jenny Backus, a Democratic strategist in Washington. “It’s something the Republicans have benefited from in the last couple campaign cycles. It allows Democrats to look moderate. A vocal left keeps the party from drifting toward triangulation.”

Democratic leaders in Congress and presidential campaigns said they winced when they saw the MoveOn advertisement. While they may have agreed with its overall point, that the troop buildup has not worked, several Democratic officials said privately that the advertisement had been counterproductive.