Is there any evidence that the GOP would increase the proportion of the Hispanic vote if they support amnesty or other immigration reforms?
A recent Pew study found that
among Latino immigrants who are not U.S. citizens or legal permanent residents (and therefore likely unauthorized immigrants), some 31% identify as Democrats and just 4% as Republicans. An additional 33% say they are political independents, 16% mention some other political party and 15% say they “don’t know” or refuse to answer the question.
In 1986, Reagan signed sweeping immigration reform into law. In 1984 37% of hispanics voted for Reagan and in 1988 25% voted for George H.W. Bush. The only Republican since 1984 to beat the 37% number was George W. Bush in 2004 with 40%. More numbers here.
This study, however, has some interesting data that shows there is a chance a Republican supporting currently discussed immigration reform laws is likely to receive a higher portion of the hispanic vote.
Thus it seems that there is evidence going both ways.
Does exit polling show that the Hispanic population match Republican positions on issues?
This isn't an exit poll, but Pew did some research related to the question. Here are some relevant parts of the report.
Some 32% of Hispanics and 34% of all U.S. adults say their political views are “very conservative” or “conservative.”
Hispanics are more likely than the general public [75% vs 19%] to say they would rather have a bigger government providing more services than a smaller government with fewer services.
On more specific issues:
Hispanics hold a more conservative view of abortion than the general public. More than half (51%) of adult Hispanics say abortion should be illegal in most or all cases, a share greater than that (41%) observed among the general public.
When asked whether homosexuality should be accepted or discouraged by society, majorities of Latinos (59%) and of the U.S. general public (58%) say it should be accepted. Meanwhile, 30% of Latinos and 33% of the general public say homosexuality should be discouraged.