Take as long as you like exploring. As far as I know only travelers like the traders move around. Other than that nothing else really changes with time. Most quest related NPC's will just wait forever untill you talk to them and activate the next stage.
There is one quest that comes to mind that is influenced by time. I'll put it in spoilers so I won't ruin your game experience, so don't read it if you don't want to know anything about future quests.
Spoiler Much later in the main quest line there will a quest available related to Vault 101. I never went there in one of my first playthroughs and the quest eventually disapeared for me. This is the only one I can remember.
Sounds about right to me, and I don't think there are any pressures to complete stuff within a given timeframe overall.
However there are situations where timing is very important. Without wanting to spoil I hear it's possible to complete the ghoul Ten Penny quest and shoot em in the head quest but it requires you to do things quickly before the window of opportunity dissapears..... (I usually balls it up somehow though!)
The main things you will notice from the passing of time is Hostile settlements might calm down, traders re-stocking and some re-spawning enemies.