(versus "Uh, no"--which confirms Obama is ready to use force against currently American citizens... or "Yeah, sure" which opens the option entirely).
Anyone who thinks it would require federal government intervention to keep this from happening (and, therefore, means what you say it means) really needs a reality check on the whole situation.
It'd probably be defeated by the citizens of each individual state, but then each state might have citizens petitioning independently of the others. That means that, while 49 states may have a referendum & decide NOT to secede, the 50th could instead secede. And success/failure of that state (and the federal response to it) will rally and change the opinions of both secessionists & federalists.
The reality is it won't happen on November 12, 2012. But, the time is coming where it COULD happen. Every political entity in history has had numbered days: the USA (and all others) will have to join that list one day or another. It may take decades or centuries but, one day, the USA will cease to exist.
That would be relevent, except you're missing one very, hugely, exceedingly, astronomically important fact: This isn't the state governments. This is private citizens acting on their own, without any kind of state government support.
The federal government wouldn't have to do **** if these private citizens decided to try and secede anyway. The state governments would take care of it much more quickly and easily.
There are already citizens who have convinced themselves that they've opted out of the federal system. Except, these "sovereign citizens" are now considered a domestic terrorist group regardless of their actual intentions or state philosophies. Guess what--things aren't all rosy, and the states that joined the USA either existed as independent entities before or as territories that opted to join.
"xxx couldn't survive on its own" arguments are completely wrong. If you say these state can't survive peacefully on its own, then which states can?
Eh? I take it you are interpreting my "Lincoln should've just let 'em secede" remark as "they would've rotted and collapsed"? I was thinking it, but I didn't say it 
But the South wasn't just a bunch of separate states. And if these states were to secede today, I doubt they would remain separate either.
That said, I don't know whether the CSA formed before or after the whole Fort Sumter debacle.
Edit: @Scotty: The fact that an actual secession is not going to go anywhere is irrelevant to what I believe Bob-san is saying. The actual petitions may be in the form of "we want to secede", but by asking Obama instead of their state governments, it's effectively forcing him to make a policy decision RE: "if our state government votes to secede, can we do it peacefully?" And Obama would have to be stupid to give an un-qualified "yes" or "no" answer, for reasons Bob-san has already addressed.
They might rot & collapse, but I think that (if the US government fell apart tomorrow & 50 states were now individual countries) only some of those states will rot & die while others will find the correct balances to survive--perhaps founding new regional confederations and perhaps rebuilding the USA in a new image.
Yes, they're forcing a policy decision. Or at least trying to. The Texas petition is sufficient to rile some support for secession--this may become a game of chess for those secessionists and the Federal government. It's been nearly 150 years since the Civil War--and the secession question's bloody answer apparently needs revisiting.
The scary truth of it all is that the Federal government and the Presidency especially has acquired a LOT of new power in the past 50 years. Phony wars and partisan politics have resulted in Bush & Obama having a LOT of power. The scariest powers, in my book, are to spy on American citizens without warrants and to administer a "kill list" which, in the past, has targeted American citizens overseas. If for no other reason than those two issues, I'd say it's high time nullification occurs and the States resist the federal government.