I do not know if this is possible but I think the online team death match is too fast? The game ends every 10-20 mins when the score is reached. Is there a way or a mode that let's you play indefinitely without scoring or at least to join a game with extremely high score goals? Currently I have no choice and I am automatically joined in a random game. This is PS3 btw.
In private matches, you can customize the rules of the game and change things such as the time limit and score limit. However, you must then invite friends to play with you. Private matches are just that - private, and only open to the people you invite.
If you're looking to play a game against random people on the internet, you are limited to the playlists that are available within the game. None of the available multiplayer game modes are time-based in Modern Warfare 3.
That said, Team Deathmatch games tend to play pretty quickly, but if you just want to be playing and getting kills, you might try an "objective" game type.