Managing people

It's been a great experience managing people. I have managed people in the past, but now taking a team of 5 is a different ball game.
It's been interesting in the last few days with 1 of them. She is roughly the same age as me and as been in the company for the same ammount of time, though not progressing as much.
She is now in charge of a project that is due to be presented to a larger team in a few days.
She is a clever girl and has good experience, but lacks in attitude. She can do some work but when faced with difficulties, just goes negative. And most of the times goes to people for help, so that people do things for her.
As her boss, I have been supportive in the last days but am now finding that I need to take a step back. I am now letting her go negative and start complaining, but letting her on her own. If it goes wrong, it will go wrong and my image will be damaged as well but... she will learn responsability and will learn not to rely so heavily on others - who have been doing a lot of work for her.

I am going to get an image of 'bad guy' with some people for this but... if I keep helping her things will go well but she will not progress professionally, she will not take any responsability and she will not get out of her confort zone. If I play 'bad guy' and make her work and 'suffer' a bit, I will get 'bad press' but definitely make her a better worker.

Definitely going for the 2nd option.