Perhaps. But Dukakis knew Spanish and he gave speeches in Spanish 'cause he was courting the Latino vote. Because of the border snafu, he could have cornered the Latino vote: being fluent in Spanish, ergo, Latinos would figure he knows their problems and respects their interests. And with that, he could have sewn up the nomination.
I don't think that Dukakis can just shore-up his candidacy and win the Dem presidential nomination with Latino votes, not in that era--and not if the political climate during Reagan's 'nights of the INS long knives'* has weakened the very rationale for his candidacy. Anyway, Jesse Jackson has a lot of (but not all of) the Latino activists in his Rainbow Coalition. I don't see him releasing his delegates to a weakened Northeastern candidate.
But there is one part of the Democratic Party that can make a nominee who is willing to appear to be firm on the border issue in this hypothetical '88 race. Organised labor. And they're not going to go with someone who looks like he might pander to the seemingly unimportant Hispanic vote.
They'll go with someone who can plausibly hedge his bets on the issue--Gephardt, Babbitt, Gore--not an ACLU liberal academic. So unfortunately you don't get Dukakis to kick around in that election**.
*Ugly rhetoric would be the tone of the season, in both parties, and in both pro- and con-deportation factions.
**Anyway, others here have convinced me that the issue isn't going to come to a head. The original poster is amiss when he fantasises about the Gipper signing an executive order that secures the border and busts all the bad guys