You can turn off the timer or hide it in your tactics trainer settings.
Enjoy!
Untimed tactics trainer
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Chess.com has the daily puzzle, and you can get more untimed puzzles in other sites and tatic books too.
Oh, I didn't see Erik's post.
Do that!
I would stick with the timed trainer. Tactics is about seeing and recognizing patterns. Petrosian once said if you don't see a tactical idea in the first minute you probably are not going to see it. The trainer is to help you develop a batting eye. Repetition is the key. Better to do ten (even if you don't solve any) than spend all your time on one.
I suppose this idea will go over like a lead balloon, since it would involve a lot of work. But anyways, I'd like to have an untimed tactics trainer available because all I play now is online chess and I'm not that concerned about being able to solve problems in under 2 minutes or whatever the TL is for each problem. I'm more concerned with getting them correct even if it takes me several minutes, since it usually isn't necessary to analyze an online game position in two minutes or less. Of course, I guess if you aren't too concerned with your "problem solving" rating this is a moot point anyways...