Yes there's a time limit, it's a very difficult game if you're not good at puzzles.

In the main game the time always moves on. There is an arcade machine in the bar with another 60 puzzle stages where you have a limited number of moves instead of a time limit. (very addictive little game)
You might have to try some main stages a couple of times to learn the best route. You can't see that far ahead anyway so standing still doesn't help much.

Catherine was an AMAZING game!!!!

Quite the contrary. If you stand still, the blocks below you will fall, line by line. Eventually, those you stand on will fall as well, along with you. The game's learning curve is steep and uneven. In the beginning you'll have no problem. You'll move like a boss. As the game progresses, you'll find puzzles much more demanding.

There's the easy mode though. You'l be OK there and you'll have the full experience the game has to offer. That is because the puzzles are merely the (lesser) half of the game. The other, greater (as far as I am concerned), half is the cutscene/interaction experience. You'll come against tough, adult decision and watch some pretty interesting dialogues. All in all, you'll successfully gain the feeling of merging into the bar and your friends' company. You'll live the story in your unique way and - pay attention here - make some breaks by playing the actual puzzle stages. Remember, this game is all about the story.

Good thing is, the puzzles are very tough and interesting, especially in the latter stages. It's a remarkable combination of demanding gameplay and catching story. If you finish it on easy, my guess is you'll try again in raised difficulty and forget all about time limits. So, the best thing is to rent it and judge for yourself, whether all these attributes appeal to you or not.

PS 2 Where the damn is that waitress-loving attorney!?

Here, here. Damn, I just got home

People (Like kabamarutr up there ^) has already explained how the "time" works. There's no...time, per see, but instead you're constantly pushed to keep moving forward because if you stand still, eventually, the blocks you're standing in will fall into oblivion (and if you fall too, that means game over).

There's checkpoints, there's retries and you even have a button (which you can't use if you play in Hard) that allow you to "undo" any dumb moves you've made (so in a sense, you don't have THAT much of a pressure; still, you need to be fast sometimes).

If you do think the game is pretty hard (even on easy), depending on where you live you may have access to the Very Easy mode (if you're from Europe, you can imput a code and allow you to go to the Very Easy mode too). In this mode, you're able to climb blocks from three to three (you can only climb one block on the other difficulties) so that you can experience the Story without getting too much aggravated with the climbing sections.

You don't have to worry. Time won't affect your experience. When you are on the bar, you have no time. (Though people won't stay forever in the bar, so make sure you interact with them before they go. In any case, you can spend time at the bar as much as you want). Trust me, you'll enjoy the game ;)