Two things are at work:
The young, more Americanized Hispanics, like immigrants before them, are much more open to Bush and Republicans than the poverty pimps that put themselves forward as "Chicano Leaders." There are certain stereotypes about Latinos that I find contain a grain of truth: (1) They love strong men and fiery women; (2) they are big on family; (3) They take pride in themselves and things they identify with, and they tend to be extremely loyal. So it would be folly not to reach out to them.
That said, I think the amnesty plan was and is a political turkey. After looking it over I believe that Mr Bush knows it's a turkey and understands it may make a one-termer of him, but sees it as The Right Thing To Do and The Best Imperfect Answer To A Hard Question. We can't just round up illegals and throw them in camps; for one thing, there's too damn many of them. Some FReepers talk that smack, but no American President could do it. Look at the flak he is taking for keeping some of the most noxious evildoers on Earth on ice in Gitmo. (Expect a new storm of hand-wringing about Haitians).
The underlying problem is that Mexico, which could be just as great a place to live and work as Texas or California, is going to continue to be screwed up as long as a small oligarchy ("paging Señor Fox...") can rip off the nation ("...the statements from your Swiss numbered accounts are in, Señor...") and keep it backward ("...and the campesinos have no tortillas"). The US will be the safety valve for unemployed Mexicans until Mexico reforms (read, "Hell freezes over").
d.o.l.
Criminal Number 18F
It is demographics! Why do you think the GOP is making a move for these voters? Their average age is much younger than other nationalities. Older gringos die, and even if the hispanic population stays the same, their share of the vote goes up. However, latino women are incredibly fertile, so their population has increased too.