The Rode Island Senate race is becoming like the CT Senate race. Incumbent Senators being seriously challenged by the "Red Meat Eaters" of the parties. If the incumbent Senators switch to Independents, those Senate races become tossups for all parties involved.
If Lieberman runs as an Independent I think that'll be a pure Toss Up, but if Chafee runs as an Independent I think that'll be Likely Dem. I just don't see how Chafee gets the math to work out as an Independent if he cannot win the GOP primary. In Lieberman's case, he'd get a lot of GOP votes, but for Chafee I don't see why any Dems who are now planning to vote for Whitehouse would switch to Chafee just because he ran as an Independent, and certainly no Laffey voters would switch to Chafee for that reason.
If Chafee cannot get a majority of the GOP leaning vote and also cannot get a majority of the Dem leaning vote then I see no way he can win as an Independent. The math just doesn't work out.