Because Connecticut has a Republican governor, who would appoint his replacement, giving the Senate 56 Republicans and 43 Democrats.
It would like be a Republican like Olympia Snowe, though, that gets appointed.
The Republican governor of Connecticut is exactly the reason why Lieberman wouldn't resign his Senate seat. And Karl Rove is way too smart to even consider this as a possibility. This speculation is ridiculous. Someone has too much time on their hands.