I think the issue is also tied to production cost in the US. Higher tariffs are, in and of themselves, depending on their severity, problematic and cause real economic distortion. (example: The Bahamas has a really screwed up economy because of the extremely high import tariffs)
That said a slight rise in tariffs AND cost control measures such as reducing corporate taxation in the US plus perhaps a national right to work law to reduce excessive union demands might reduce imports and stimulate domestic production.
To the best of my knowledge the Bush raise in steel tariffs did not also include a reduction in corporate taxes
Yeah, what I remember is that all Bush wanted was a "new tone" and to "reach out across the aisle". All that came of it was the Dems bit his hand off.