can the president and the vice president come from the same state
No. The Constitution doesn't allow the electors to choose both a vice president and a president from the same state as the elector. This provision is easily sidestepped when one of the candidates changes his legal residence to another state -- as Vice President Cheney did.
http://library.thinkquest.org/12405/14start.htm
http://www.thegreenpapers.com/Hx/ConProv.html
Ooops -- I posted the wrong link. The library.thinkquest link does not pertain to this question.
Sorry.
The Twelfth Amendment does not preclude the election of a President and Vice President from the same state. Nevertheless, running mates conventionally come from different states to prevent situations wherein electors of the state in question are forced to vote for a candidate from a different party merely on the grounds of residency. The issue arose during the 2000 presidential election contested by George W. Bush (alongside running-mate Cheney) and Al Gore (alongside Joe Lieberman). It was alleged that Cheney and Bush were both inhabitants of Texas, and that the Texas electors could therefore not cast their ballots for both. Bush's residency was unquestioned, as he was governor of Texas at the time. Cheney had lived and was registered to vote in Texas, but a few months before the election changed his official residency to Wyoming, the state where he had grown up, and for which he had, many years earlier, served as the U.S. Representative. A lawsuit alleging that Cheney remained an inhabitant of Texas was brought, but it was dismissed by the U.S. District Court for the Northern District of Texas.
Source:
http://www.answers.com/topic/amendment-xii-to-the-u-s-constitution