PORTLAND, Maine — The third big-name Democrat to consider a Senate run in Maine — former Gov. John Baldacci — expects to take his time before announcing any decision because his current Pentagon job poses an obstacle to a possible candidacy for now.

Baldacci, 57, is prohibited from politicking while he wraps up a Pentagon contract this month, potentially delaying his announcement on whether he’ll enter the race, which was thrown wide open by Sen. Olympia Snowe’s announcement last week that she won’t seek a fourth term.

In the span of little more than a week, Reps. Mike Michaud and Chellie Pingree, who were both weighing a run, bowed out to focus on defending their House seats instead.

Baldacci hadn’t made up his mind as of Thursday but couldn’t talk about it publicly even if he’d made a final decision, said his spokesman, Dan Cashman.

Behind the scenes, however, signatures were being collected on Baldacci’s behalf and could be submitted before next week’s deadline to appear on the June ballot. If he runs, Baldacci would be a strong candidate, having been elected twice as governor and three times to the U.S. House, Cashman said.

“Gov. John Baldacci has a pretty successful record when it comes to running a campaign,” he said.

Snowe’s announcement last week that she wouldn’t seek a fourth term set off a scramble because potential candidates for the soon-to-be empty seat face a March 15 deadline to submit 2,000 signatures to get on the June primary ballot.

Michaud expressed interest in the empty seat before announcing 48 hours later that he’d stick to his northern congressional district. Pingree followed suit less than a week later after former independent Gov. Angus King announced he was running.

Baldacci and Democrats face a tough choice, because if they lose, they could end up splitting the vote with King, giving a boost to the Republican in the race. That’s what happened when Republican Gov. Paul LePage won with 39 percent to 37 percent for independent Eliot Cutler in 2010 in a three-way race. Like Cutler, King is a former Democrat.

“I think it’s a catch-22 for the Democrats because if they run a strong candidate, they run a risk of losing the election. If they run a token candidate, they put their faith in Angus King caucusing with them,” said Michael Franz, professor of government at Bowdoin College.

Four previously announced Democrats remain in the Senate race: former Secretary of State Matthew Dunlap, state Rep. John Hinck, state Sen. Sen. Cynthia Dill and home builder Ben Pollard.

Dunlap said he understand that candidates with greater name recognition like Pingree and Michaud had to give the race a look. For now, he said, he intends to stay in the race regardless of Baldacci’s decision. He said he’s at peace with the changing competitive landscape.

“All we can do is push forward on the campaign. You can’t wait to see what others are going to do. I’m committed to getting down there and making a difference,” he said.

On the GOP side, Scott D’Amboise could be joined by Treasurer Bruce Poliquin, Attorney General William Schneider, Secretary of State Charlie Summers, state Sen. Debra Plowman of Hampden and former state Sen. Rick Bennett, all of whom have expressed interest.