Although not facing the same deadlines as their potential major-party rivals, former Gov. Angus King and former gubernatorial candidate Eliot Cutler expect to decide by next week whether they will run for Sen. Olympia Snowe’s seat as independent candidates.

Political observers, meanwhile, said an independent candidate — and particularly King — could have a major impact on what will be Maine’s most hotly contested U.S. Senate race since 1996.

King said Thursday that he is talking with people in both Maine and Washington, D.C., as he attempts to figure out whether he could make a difference on Capitol Hill or whether “it is hopeless down there.”

King, who served as governor from 1995 to 2003, said the partisanship and divisiveness that prompted Snowe to drop her re-election bid would be his major reason for running. But the question he is asking right now is whether there was some way that he, as an independent, could help bridge that two-party gap and help change a broken system.

“To be honest, I am trying to figure out whether I can make a difference down there,” King said Thursday. “If I can, then it is worth it … But I don’t need to be a senator. Is it possible to make a difference or is it hopeless down there?”

Cutler, who finished second in the 2010 gubernatorial contest, agreed with King that this is the one electoral instance in Maine where independents have an advantage over major-party candidates. That is because independents have until June 1 to collect 4,000 petition signatures to qualify for the ballot while party candidates must collect 2,000 signatures by March 15.

But Cutler said being coy is not his strong suit, so he expects to decide by sometime next week.

“I am committed — deeply committed — to rebuilding the political center and reforming the political process, and I am committed to serving the people of Maine,” Cutler said in an interview Thursday. “The question is what is the best way to do that? Is the best way to run for Senate? Is the best way to run for governor of Maine again? Or is the best way to continue what I am doing?”

For her part, Snowe has said she does not foresee the partisanship changing in the short term but that she believes she could help build support for that change outside of the Senate.

King won his first election as governor in 1994 by capturing roughly 35 percent of the vote in a five-person race, becoming Maine’s second independent governor. King easily won re-election four years later.

James B. Longley, the state’s first independent governor, served one term after being elected in 1974.

While independents ran for U.S. Senate in Maine in 1994, 1996 and 2006, none of those candidates received more than 6 percent of the vote. Cutler and especially King likely would have a much bigger impact, observers said.

Douglas Hodgkin, a retired professor of politics at Bates College, said he believed King would be “an immediate contender.”

“He was a very popular governor and was re-elected by quite a margin,” Hodgkin said. “I believe he would have enough money. And there are also substantial numbers of voters who are unenrolled, so that independent designation would be appealing to some Maine voters.”

MaryEllen FitzGerald, president of the Portland-based polling firm Critical Insights, said she does not see King as “having a lot of negatives” if he decided to run, at least initially. He largely walked away from politics after leaving the Blaine House and would be able to disassociate himself with the current partisanship, she said.

“I think he was seen as a good leader and as a very articulate spokesperson,” FitzGerald said. “I think he engendered trust on both sides of the aisle.”

Of course, during a political campaign, opposing parties would be sure to mine King’s eight-year record as governor for potential political liabilities. And with the Maine race suddenly critical to the power balance in the Senate, national GOP and Democratic campaigns are expected to spend large sums in the Pine Tree State — with some of that money likely targeting King if he were viewed as a threat.

Cutler could have an impact in his own right, judging by his second-place finish in the 2010 gubernatorial race, just 2 percentage points behind Republican Gov. Paul LePage. Although lesser known than King, Cutler has stayed in the public eye, to some extent, since November 2010 by his participation in the No Labels and Americans Elect campaigns to support candidates that shun party labels and ideology and will work across party lines.

“People in Maine very much want a choice and very much want one of us to run,” Cutler said of himself and King.

Cutler’s success in 2010 was due in part to the fact that some loyal Democrats perceived him as having a better chance to defeat the conservative LePage than the Democratic nominee, Senate President Libby Mitchell. Hodgkin said that as a result he believes King would be the stronger of the two because of his reputation as governor.

Either King or Cutler — or both — inevitably would face criticisms from some Democrats concerned that their candidacies would aid the Republican nominee by dividing Maine’s moderate and liberal voting blocks. King apparently has already heard some of those arguments but said Thursday that they are not a factor in deciding whether to enter the race.

“I tell people, ‘The last time I ran I wasn’t a spoiler, I was the winner,’” King said.