Maximum number of moves

Is there any limit on how many moves a game can last?  If the game hits that limit, is it declared a draw or is there a win based on pieces left on the board?  I ask because my opponent is currently spamming check with no intent to go for mate and keeps offering me draws.  I admit, I made a mistake that got me into this position, I just want to know if there's a point in continuing because I'll automatically win at 100 moves or if I should just take the draw.  I really don't want the draw because I beat this guy and just screwed up one move.

See Article 9: The drawn game. http://www.fide.com/component/handbook/?id=124&view=article

hmhill17, please also refer to the Chess.com rules page at http://www.chess.com/learn-how-to-play-chess.html#draws where the special draw rules such as the 50 move rule is explained.

If you screwed up just one move than you obviously didn't have him competly beat, the game isn't over until your opponent resigns

Well, sort-of, as there is a limit of 50 that can be made without moving a pawn of capturing a piece.