A palmetto is a type of small palm tree. Like big palm trees, palmettos grow in warm places — places like South Carolina, for instance. Back in 1860 when Abraham Lincoln was running for president, South Carolina was a committed slave-holding state that didn't like the sound of honest Abe's plans to limit slavery in the U.S. In fact, the state threatened to secede if he became president.
South Carolina made good on that promise in December 1860 in the wake of Lincoln's historic election, becoming the first state to secede from the union. The secessionists declared themselves an independent country known as the Palmetto Republic. Well, this was actually the Second Palmetto Republic. The good people of South Carolina had declared the first one nearly a hundred years earlier in 1776 during the lead-up to the Revolutionary War.
The Second Palmetto Republic didn't plan on going it alone for long. In short order it persuaded the other slave-holding states to secede as well. In February 1861, South Carolina and six other states created the Confederacy. The 2nd Palmetto Republic had endured for just two months [source: Woodworth and Winkle].
Memories of that brief nation have inspired modern-day secessionists to call for the formation of the Third Palmetto Republic. Maybe they'll manage to get a referendum going — Palmexit has a nice ring to it.