Are there always enough keys on a level?

Unfortunately, no.

In my experience, there won't always be enough keys for every door. There will be a few times when you get 2 keys, but there will be 3 locked doors, requiring you to try and decide which (if any) door you want to open.

The exception to this rule is the Skeleton Key which can be found randomly in the treasure rooms or challenge rooms (kill x number of enemies after opening a chest). It awards you with 99 keys, which is enough to open ALL the doors (assuming you don't get the Bombs are Key pill).

In my play throughs I've run into situations where there are simply not enough keys in the level to open every lock or chest.

There are several ways to get keys but you might not be able to get enough in a level so use them wisely. My best suggestion is to use them on the item rooms, shops (if you have enough money to possibly buy things), golden chests, and lastly, locked blocks, in that order with some exceptions.