I've actually never had a huge problem with self-funded millionaire candidates - it's a problem with the system not with the candidates themselves. Of course I'd prefer a system where that wouldn't be an advantage, but frankly given the current system we have the "self-funded millionaire" is actually one of the few ways to get around the bigger problem of the power of entrenched incumbency.
In any case it's rather amusing the Lieberman is a WATB about millionaire candidates even though he's supported them wholeheartedly in the past.
It inspired me to take a look at where Joe's support has come from in the past. In his 1994 election campaign (.pdf) fully 87% of Lieberman's came either from PACs and from large (over $200) donations, with only 8% ($409,504) coming from individual donors giving under $200.
Over the 2000 campaign (admittedly an odd campaign due to the fact that he was also running for VP), only 4.5% of his money came from small donors ($193,562 total).
Opensecrets hasn't broken out the numbers yet for the latest campaign season.
I can't break out Lamonts numbers completely yet, either, but as of the latest filing he's given $371,500 of his own money to the campaign and raised $405,380 otherwise entirely from individual donations.
We also know from his total ActBlue donations that he's raised about half of that through that site, or $205,922, rom 4142 individual donors. That's an average of about $50.
Anyway, the point is WATB Joe has a history of relying on The Big Money to support his campaign, support which is generally only possible to obtain if you are the incumbent. Ned's donated some cash himself, but it seems he's raising money from the little people much more than Joe ever did.