First, if you look at all the temporary tariffs (i.e., the kind Obama just announced for Chinese tires) imposed in the world between 2000 and 2008, you see that the number in 2008 was well below the average across all those years (155 versus 189). Not so in the United States, though. We were of the few major economies in which the number of temporary tariffs exceeded the 9-year average in 2008 (30 versus 23). Three guesses as to who was president back then... (For what it's worth, I note this only to highlight the trajectory of U.S. trade policy before Obama became president, at least as it relates to temporary tariffs.)
Second, while it's true that Bush never specifically imposed a "Section 421" safeguard--that is, the tariff at issue in the Chinese tire case--he did impose a very similar type of safeguard on Chinese linens and clothes in 2005, which went into effect the following year. Safeguards tend to rile up free-traders because they're not a response to unfair trade practices per se (like dumping), but simply to a surge of imports from another country, which can happen for entirely legitimate reasons.
The point, again, is not that Bush was some closet protectionist. Just that it's pretty unfair to conclude from the tire tariff that Obama is. The move certainly didn't justify the kind of rhetoric was saw in response, like The Journal's comparison of Obama's trade policies to Herbert Hoover's.
Update: The DLC's Ed Gresser emails to make another great point: Bush's real lapse on trade wasn't the 2002 steel tariff or any other temporary tariff, all of which expire after a couple years. It was the 2002 farm bill, which entrenched a lot of agricultural subsidies that are anathema to our trading partners and would-be trading partners, and are a key reason he didn't make more progress on multilateral trade deals as president. (To their credit, many conservatives were pretty exercised about the bill on free-trade grounds.)