That is an extremely charitable parsing of the events. The more accurate (realpolitik) version is Bush said the no new taxes quip, and Democrats subsequently laser-focused on making him (slightly) raise taxes, showing he is a "liar".
My take away is to learn not to promise overly optimistic outcomes when your political rivals have a significant stake in seeing you either be a success or a failure.
Edit: Not sure why this was flagged. Did not mean to come off as hostile or aggressive. Anyways, cheers.