Actually the Bill or Rights:
Ninth Ammendment
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
Comment: The Ninth Amendment declares that just because certain rights are not mentioned in the Constitution does not mean that they do not exist. Courts may not infer from the silence of the Constitution that an unlisted right is unavailable to protect individuals from the government.
Tenth Amendment
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
Comment: The Tenth Amendment restates a fundamental constitutional rule: If a particular power was not assigned to the federal government by the Constitution itself, then the states may exercise the power, unless the Constitution also prohibits the states from exercising it. The Tenth Amendment also states that people are free to act, without permission of the federal government, in areas outside the scope of the federal government's powers.
Moreover the Declaration of Independance from Britain sets a precedent. Here is a link to the text
http://www.law.indiana.edu/uslawdocs/declaration.html
Note the first section of the second paragraph.
Now the real question. Would the federal government fight back. On this point you almost assuredly can be assured they would, especially if it were California New York or one of the other large economic powerhouses that wanted to seceed. However the right is there.
Would the Eu have fought back or agreed in the EU Parliment had say Germany wanted to leave the union? Seeing as how it is the economic giant of the union and its leaving would almost assuredly mean the demise of the union itself I am willing to bet the European Parliment would not have voted to allow it, unless Germany gave the EU very very very favorable terms. THe issue isn't if the paper says a state has the right, the point is what will the federal entity at the top of the chain do once a state indicates it wants to leave.