Correction appended

Sen. Joe Lieberman said Friday afternoon that his central role in the push to repeal the military’s “don’t ask, don’t tell” policy banning openly gay service members would not preclude him from running as a Republican in 2012.

While much has been written in recent days suggesting that the Connecticut Independent is using the issue to solidify his Democratic credentials before a difficult re-election bid, Lieberman said the timing was simply “a coincidence” and his position could help him with voters across the political spectrum.

He spoke to Roll Call briefly after leading a Capitol Hill press conference Friday afternoon with the pro-repeal group Servicemembers Legal Defense Network. The vote on repealing the Bill Clinton-era policy is expected Saturday.

Asked if his pro-gay-rights stance would make it impossible to run as Republican, Lieberman could have ruled out such a possibility. But he didn’t, saying instead: “I don’t know about that.”

“I think out there in the public, the support generally for ending discrimination against people based on sexual orientation, and particularly in the military, is widespread and crosses party lines, probably still more among Democrats and independents than Republicans, but a lot among Republicans,” Lieberman said.

He has yet to say whether he will seek a fifth term, and, should he run, under which political affiliation. Asked about his plans Friday on MSNBC, he said “all options are open,” adding that he was leaning in one direction. “I’d say right now if I run again, it’s more likely I’ll run as an Independent.”

After losing Connecticut’s Democratic primary in 2006, Lieberman left the party and mounted a successful campaign as an Independent. The move, and his subsequent support of Sen. John McCain (R-Ariz.) for president in 2008, fueled deep resentment among Nutmeg State Democrats that lingers today.

That’s in part why Lieberman has no easy road to victory in 2012. Roll Call Politics rates this race a Tossup.

Political strategists from both parties expect him to struggle in a Republican or Democratic primary. And the electoral math may not allow for a second successful Independent bid, largely because stronger candidates are expected from both parties in 2012 compared with 2006, when the GOP ran only token opposition, allowing Lieberman to capture much of the Republican vote in his victory.

Linda McMahon, the independently wealthy, unsuccessful 2010 GOP Senate candidate, is among those who may enter the mix in the coming cycle. National Republican Senatorial Committee Chairman John Cornyn (Texas) recently told Roll Call that he and McMahon will meet privately in the coming weeks.

Lieberman has been among the Senate’s strongest and most public supporters of the DADT repeal effort in recent days, fueling speculation that he was trying to win back Connecticut Democrats.

Asked Friday whether that was the case, Lieberman told Roll Call, “It is coincidental that the effort to repeal ‘don’t ask, don’t tell’ reached this stage at this point. I’ve been against this since 1993. I actually voted against it in 1993 on the Armed Services Committee.”

He added, “I feel a tremendous sense of satisfaction that I’ve been able to play this role in ending a policy I think is basically just un-American.”

Correction: Dec. 17, 2010

The article originally stated that Lieberman has not decided whether to seek a fourth term. Lieberman would be seeking his fifth term if he were to run again.