I'm having a hard time progressing because the remaining enemies simply have way more units than I do. The thing is I have tons of gold and resources. If I just click "next turn" a whole bunch of times I will end up with a ton of units. Are there any consequences to sitting still and doing nothing? I'm afraid if I do nothing for a bunch of weeks except waiting for new units to be generated that there will be negative consequences.
If you spend longer on a campaign map, you will get a lower score, so that is one potential negative.
Also, you have to make sure that you army is growing faster than your enemy's, or you will never get to a point when you can beat them. The simplest way to do this is to look at the difficulty of a particular enemy you want to defeat. If that difficulty ever decreases, your army is probably growing faster. Similarly, if it ever gets more difficult or it stays the same for a long time, then the fight probably will never get easier.
I used this strategy in the first Necromancer campaign mission on Normal difficulty with the following results:
This implies that the opponent's displayed difficulty can sometimes be a useful heuristic, but it is not a definite indicator of relative army strength.
If the enemy is sending heroes to kill you, remember to stay in your town to take full advantage of your fortifications, and remember to pay attention enough to buy units before you get attacked or you might get surprised by a superior force. If you can make him sustain a lot more losses, you might be able to gain an advantageous position faster.
I totally agree with the accepted answer.
However, there is an achievement that requires that a replay of a campaign is faster than the previous time.
So actually it might be a good idea to waste time during the first play-through :)