mission creep

(politics, military, idiomatic) Gradual expansion of the objectives, scope, and/or cost of a military mission without careful planning.

Example: 1994 Sep. 19, Mark Thompson, "Haiti: The Past As Prelude," Time:
  Initially presented as a purely humanitarian mission, Operation Restore Hope gradually shifted from feeding Somalis to fighting them. Unaware of the "mission creep," the public was outraged when 18 U.S. soldiers died in an October 1993 fire fight.
1995 Oct. 23, Elaine Sciolino, "One-Year Limit on U.S. Troops in Bosnia Now an 'Estimate'," New York Times (Retrieved 27 May 2011):
  General John Shalikashvili . . . said it was important to set a target date of one year and then bring the troops home, because "in the absence of that, you find yourself staying there, and that's how very often mission creep comes in."
2011 March 13, Ramesh Thakur, "Acting responsibly to protect Libyans," Toronto Star (Retrieved 27 May 2011):
  The risks of mission creep and a deepening quagmire leading to nation-building would arise only if ownership of the uprising was appropriated from the Libyans by the West, as would happen with ground troops.