Rick Perry may not be able to run...

According to the Huffington Post on April 4, 2009 - "...Perry called his supporters patriots. Later, answering news reporters' questions, Perry suggested Texans might at some point get so fed up they would want to secede from the union, though he said he sees no reason why Texas should do that.

"There's a lot of different scenarios," Perry said. "We've got a great union. There's absolutely no reason to dissolve it. But if Washington continues to thumb their nose at the American people, you know, who knows what might come out of that. But Texas is a very unique place, and we're a pretty independent lot to boot."

In reading the 14th Amendment to the Constitution, Section 3: 

No person shall be a Senator or Representative in Congress, or elector of President and Vice-President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may by a vote of two-thirds of each House, remove such disability.

Even the mere suggestion of secession by an elected official, may be grounds for disability to run for the office of President of the United States depending on interpretation of this amendment.  There appears to be a clear difference between engaging in insurrection and the act of treason and treason would fall under the the heading of rebellion in the above listed amendment.