Huckabee, himself a migrant to Florida, is probably worried for nothing. That's because the long history of New Yorkers moving to Florida has actually coincided with the state growing more Republican, not less.
In 2014, the New York Times published a state-by-state look at migration patterns based on Census analysis from the University of Minnesota. Over the past 110 years, the place of birth for Floridians has shifted regularly. It's only been about 50 years or so that they came heavily from the Empire State.
If we isolate New York (and the rest of the Northeast, just for kicks), you can see how the pattern has shifted over time.
But here's the thing: Over the course of the 20th century, Florida grew more Republican relative to the rest of the country. If you track the margin of support for the winning presidential candidate in Florida versus the rest of the country, Florida only started voting more heavily Republican in 1960 -- the same year the number of New York-born Floridians first surpassed 5 percent.
There are a few possible reasons for this. The first is that the people who move to Florida tend to be retirees. While it hasn't always been the case, older voters tend to vote more Republican. That's particularly true right now, meaning it should hardly be a disincentive for the state Republican party.
The second is that New York was becoming more Democratic as Florida was becoming more Republican. If we're assuming that migration patterns affect political voting, it seems fair to assume, then, that it was more likely to be Republicans moving South -- a bit of political self-sorting.
But the third and most important reason for Florida's voting shift is that Florida is a Southern state. Over the latter half of the 20th century, the Deep South went from dark blue to dark red. Georgia, Louisiana, Alabama, South Carolina -- all states that moved away from the Democratic party even more than did Florida. The migration of people from New York was almost certainly a drop in that demographic bucket.
As the percentage of New York-born Floridians has started to drop, the percentage of foreign-born Floridians has increased. Those immigrants used to be largely from Cuba, and voting Republican. But that population is beginning to vote more heavily Democratic, and the diverse nations of origin in Florida include other Hispanic populations that tend to vote even more heavily Democratic.
The New York line is a decent gag, but it's not the demographic shift Florida Republicans should be worried about.