I know the national GOP and conservative groups are spinning this as a rebuke of the Obama administration, and there is certainly an element of that in the significance of the Brown win, but I don't think that's the majority of the story. Local Massachusetts politics deserve attention, too.
In most parts of the country, the local party is more popular than the national one. People may think "the Republicans" or "the Democrats" are corrupt, wasteful, etc., but think their local rep (D or R) is OK. I knew many Democrats here in northeast Ohio who couldn't stand the national GOP, for example, but thought Ralph Regula (R) was a good guy. (He retired recently after something like 36 years in the House.) The situation is different in Massachusetts. The last three consecutive speakers of the state legislature (all Dems) have been indicted on corruption charges. Gov. Deval Patrick is not very popular, even among Democrats. Obama is still personally very popular in Massachusetts. If the presidential election were held again today, Obama would beat both a generic Republican candidate and any plausible GOP nominee. Obviously, however, the Massachusetts voters feel differently about their local figures.
You can look at this as a rebuke to Obama, yes. (And, on the flip side, I know many liberals who were already engaging in damage control days before the election, attempting to cabin the implications to Coakley and Coakley alone.) However, I think it's as much or more a rebuke to the Massachusetts state Democratic Party. Its track record in the state of late has been underwhelming.