As you see, there has never been a majority of Hispanics voting for a Republican president. This even when Republicans have supported or even enacted an immigration Amnesty, the issue most commonly cited as key to garner Hispanic support. The variation in Republican support is fairly small.
What turned out to be decisive in 2012 was hence the increase in the number of Hispanic voters.
Romney received 27 percent of the Hispanic vote, marginally down from Pro-Comprehensive Immigration Reform John McCain who got 31 percent. The highest vote share a Republican has received among Hispanics is Texas governor George Bush who got 40 percent post 9-11 and right before the peak of the housing boom, and hence the peak of Hispanic economic fortunes. The 40 percent Bush got was still a decisive defeat. Even though Republican President Ronald Reagan had granted illegal immigrants Amnesty in 1986, two years later only 30 percent of Hispanics voted for Bush Sr.
This ["natural Republicans"] claim is demonstrably false. In 2012 Hispanics solidly support the Democrats on virtually every issue, not only on illegal immigration. This includes taxes, the size of government, health care. Less known is that increasingly liberal Hispanics now support Democrats on abortion, gay marriage and contraception.
Why do Hispanics vote Democrat? The main reason is that Hispanics on average earn far less than Whites (henceforth "Whites" refers to non-Hispanic Whites). It is simply not in Hispanic material self-interests to vote for the party of limited government.
The main reason that people believe largely unsupported claims about Hispanics being “Natural Republicans” is that unflattering facts about immigration are considered gauche in US public debate. It is just not nice to point out that a large segment of a group is comparatively poor and low-skilled. Though confronting these facts frankly may be uncomfortable to some, doing so is crucial to the survival of the Republican Party.