Set One's Heart On Meaning

(transitive, idiomatic) To desire with intensity and commitment.

Example: 1856, T. S. Arthur, "A True Tale of Life" in The Wedding Guest:
  With all the willful eagerness of a child she set her heart on that visit, and from morning till night she would talk with her little boys of the journey to what seemed to her the brightest, most sacred spot on earth, next to her present home.
1876, Louisa May Alcott, Rose in Bloom, Ch. 5:
  [H]e always found it hard to give up anything he had set his heart on, no matter how trivial.
1972 April 3, "Religion: Heal Thy Enemy," Time:
  Roberts set his heart on a national basketball championship.
2008 January 15, "Mitt Romney’s Michigan Primary Speech," New York Times (retrieved 26 May 2013):
  Americans can do whatever they set their hearts on.