Well, never mind, because my opponent just pushed his pawn, so I can wait another 50 moves.
50 Move Rule

I did offer the draw, no luck. For like 60 moves I was defending Rook and 3 pawns vs. Rook and 4 pawns. The pawns were blocked, so there was just king and rook moves. My opponent lost a pawn, we traded rooks, and now we are in a dead drawn King and 3 pawns vs. King and 3 pawns. We've played 160 moves and he still won't accept the draw. This game may go on until it's King vs. King.
I'm playing in game (http://www.chess.com/echess/game.html?id=42409416) where we passed the 50 move rule a few moves ago and the offer draw button isn't replaced by the claim draw. Is this a bug or does Chess.com not have the 50 move rule?