That document is dated February 2005. President Bush did kind of a John Kerry number: he supported it after he opposed it. He worked very hard to get it stripped out of the 9/11 Security Bill in 2004. He wasn't given much choice but to support it in February because Sensenbrenner and the House Leadership made it clear that it was going to be attached to the first "must pass" bill in 2005 and that it would be nonnegotiable. His choices were to support it or get handed a defeat by his own party and have it pass anyway
As far as attracting Hispanic votes goes, I've always believed that the Republicans new found enthusiasm for the Hispanic vote and all of the hispandering was just a smokescreen for the real objective which is to secure an unlimited supply of cheap labor.
I think his real objective with regard to that bill was to get the border-security provisions stripped out, so he waged a general campaign against all illegal-alien-related provisions, on the pretext that these things were extraneous to the goals of the bill. I'm sure that even he knew he would look kind of silly arguing against increased funding for the BP while supporting the "REAL ID" provisions in the same bill.
I think that at heart Bush has no problem with any bill that increases federal control over traditionally state matters like drivers' licensing, especially when it provides opportunities for further surveillance and tracking of people.