The Lieberman campaign responds:

[Lieberman spokeswoman Marion] Steinfels said that Lieberman would "absolutely not" run on the GOP line. She added: "He has said he's always been a Democrat, and he'll always be a Democrat."

Asked if he'd rule out accepting the line, Steinfels said: "Joe Lieberman will never run as a Republican. Never."

This morning, Election Central posed the question in a phone call to campaign deputy press secretary Noah Kores. He said the campaign would get back to us, and we said we'd let you know when (or if) the campaign did.

Why this wasn't a no-brainer immediate response is a mystery. (Update: As Maura points out, though, Lieberman also said he would remain a Democrat while simultaneously running on the Lieberman Party line against the Democratic nominee, so can we really take him at his word about not running on the Republican line?)

Meanwhile, some state Republicans are apparently hoping that Joe will change his mind:

Others think offering the [Republican] spot to Lieberman on a ticket headed by popular governor Jodi Rell (for whom Lieberman has had much praise) would give a powerful boost to the rest of the ticket.