If they stay then the EU would have to give them additional billions without the legitimacy amongst their constituents to do so. EU politicians have to satisfy their base but this is contrary to what would be best for Greece or even the EU in the long run. Even if they would give those billions, then other countries that have financial troubles (e.g. Spain) would expect something as well. Both these things have already resulted in the EU demanding counter-productive things while giving Greece less than what was needed. On the other hand, the Greeks have been living above what they could afford for over a decade now and getting them out will force them to live with much less means than they have in the past. This would at least enable them to fix a lot of stuff they are currently doing to satisfy the EU's harsh demands.
Either way, the next 2+ years will be really shitty for Greeks.