It's easy to see why the NYT holds a grudge against Clinton. If she hadn't been so stupid to take their reporting on the buildup to Iraq seriously and vote for the war they advocated, the war wouldn't have happened and NYT wouldn't have been discredited as an organization. Clinton really should be ashamed at her complete lack of ethics in the interests of the free press.
The senate vote for the Iraq War was 77-23 in favor. Hillary (or Hillary and a few other random senators) changing her/their vote(s) wouldn't have changed anything. Sure, maybe the media would like her more. But the war still would have happened.
http://en.wikipedia.org/wiki/Iraq_Resolution#United_States_Senate