It's more than enough. In fact it's probably way too much. You generally want to spend as little time as possible at the lowest stakes and the best way to achieve that is with an aggressive bankroll management strategy.
I would only play at 2NL if you're a complete beginner at online cash games and are just trying to build up some confidence and experience at a level where the money doesn't matter to you. Otherwise move up.
If you are not a winning player, no balance is enough - you will go broke eventually. If that is the case then stay at 2NL; your balance will last longer. If you are a winning player at 2NL, you probably can win at 5NL. There is no one magic number for how many buy ins you need, but your balance at 5NL is 36 buyins. That should be sufficient almost all the time if you are a winner.
The larger your bankroll the less risk you have of going broke. It really depends on your risk tolerance and what your own financial situation is. What happens if you lose your $180? If Tony the Shark is going to come break your thumbs and kill your mother if you lose it, then yeah stay at 2NL. If you are just going to reload and try again, then probably taking the shot a 5 is worth it. If it is somewhere in between then you have to use your judgement. Also, don’t forget that if you try playing 5 and it goes badly, you can always drop back down to 2. Even with a $60 bankroll you should still be ok.
