Elizabeth Aguilera of the Denver Post offers "Dems won over Latino voters, study says":

Latino voters leaned heavily Democratic in the recent midterm elections, indicating the heated debate over immigration reform may have cost Republicans support in some key races, an analysis released Monday indicates...

...Some, however, questioned whether the study exaggerated the impact of immigration on the Democrats' wins Nov. 7...

Michelle Mittelstadt of the Houston Chronicle offers the similar "Immigration alone didn't sway Hispanics from GOP":

Exit polls suggest Latino voters deserted the Republican candidates at nearly twice the rate of non-Hispanic whites during this month's congressional elections, the Pew Hispanic Center said on Monday.

But the conventional wisdom that Hispanics were turned off by the party's hard line on illegal immigration — and would deliver on the "Today we march, tomorrow we vote" cry from the spring's protest marches — was not the decisive factor, some experts said...

The bottom line is that no one knows for certain, and it boils down to which illegal immigration-supporting hack you choose to believe.