Ultimately, no. For one thing, whoever the Democratic nominee is will have to withstand ceaseless attacks from the Republican candidate/supporters of the Republican candidate. Going through a little trial by fire now is not a bad thing.
Secondly, we’re still 10 months out from the general election. It’s very unlikely that any storylines from February, March or April will persist through the summer and into the fall.
Thirdly, it is highly likely that the losing Democratic candidate will endorse and then campaign for the winning one. It might be a bit strained, but both Senator Clinton and Senator Obama want to remain as leaders within the party and to do that means sucking it up and helping the one who beat you.
One caveat: if Clinton’s attacks on Obama are seen by many in the African American community as too unfair, it could cut into her support in the general. This could be mitigated somewhat if and when Obama campaigns for her, but it is a possibility.