Connecticut Sen. Joe Lieberman has been one of Sen. John McCain's staunchest supporters of late. Lieberman, who now styles himself as an "independent Democrat," has been campaigning hard for the Republican presidential nominee-elect. But a new poll shows that voters in Lieberman's home state may not care much.

A Quinnipiac University poll released Thursday shows McCain trailing in head-to-head contests with either potential Democratic nominee. Barack Obama leads McCain 52 percent to 35 percent, while Hillary Clinton leads 45-42. (The margin of error is plus or minus 2.4 percentage points, meaning the Clinton-McCain numbers are really a tossup.)

What the poll seems to show is that though Lieberman's beloved independent voters would go Republican in a Clinton-McCain matchup, 48-36, in the case of an Obama-McCain election, even Lieberman's campaigning might not prevent independents from flocking to Obama. Obama currently leads among independents, beating McCain 45-38.

Lieberman's personal approval ratings remain steady, however. Fifty-two percent of those polled approve of the job he's doing as senator; that number has barely changed since August 2006. (His high was 80 percent, in September 2000.) Connecticut Democrats, however, are not currently fans of Lieberman's. While he gets 77 percent approval from Republicans and 51 percent approval from independents, he's mired at only 39 percent approval from Democrats.