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 ;)
