Ask HN: How long should money the 1st investment last?

It's a bit weird situation. I got accepted into an accelerator, will go with them unless there's something I like more and there's just ~10 days left before I have to sign the papers.

I just finished an initial Skype call with two guys from a really nice VC fund (made of people who have created successful startups themselves). They like my startup and are willing to work under this unusual time pressure. My gut tells me that when it comes to non-financial aspects of the relationship, it could be better to go with them.

They asked me to send them a list of expected expenses. I know pretty well how much I'm gonna need, but I don't know how much it should last for. While I have some income and it's likely it will increase over the next 6 months, it's not guaranteed and I think I should assume it won't go up, just to be safe.

So how long do I need to be able to run on this 1st investment? 6 months? 12? 18?