John McCain and Joe Lieberman have been intertwined a lot over the last few years and here's another place where they share company—they are two of the three least popular out of the 81 sitting Senators PPP has done approval polls on since the beginning of 2010. McCain's approval rating is only 34% with 53% of voters disapproving of him. That makes him the third least popular. Lieberman is the least popular and John Ensign is the second least popular.
Lieberman and McCain have the same problem—they're not very popular with their party base but no one else likes them either.
So the only thing keeping them from being joined at the bottom is the guy who paid for the right to be the bottom.