He needed a strong Democratic Presidential candidate to be able to win re-election. Certainly with Kerry at the top of the ticket, he would have lost, in part because of his Presidential dabbling. Had he settled down and approached his Senate seat from the standpoint of a job he intended to hold until he retired, I think he would have pulled out a narrow victory, but it would be close. He certainly could not have pulled a Bentsen and run for both Senate and the Vice-Presidency.
Lieberman didn't do too badly in 2000 when he ran joint campaigns. Though obviously I know what you're getting at - an incumbent Democrat is much more vulnerable in the South than in Connecticut.
I heard that a popular nickname for Edwards in NC was "Senator Gone", because he hardly spent any time in the state. And considering he hardly ever showed up to senate votes either, it kinda makes you wonder what the hell he'd been doing for the previous six years. He would have lost easily.