Your co-founder will, hopefully, not find out about this through guessing "Is this my company?" on Twitter, but rather in hearing it from you. You may be heartbroken about it, you may cry a bit (totally OK). Then, you will put on your Responsible Adult pants, call your employee into the office, and tell them the situation. You will emphasize that it is in no way their fault. You will tell them the status of your future payments to them (you can make them -- good), and instruct them that they have no job now other than lining up their next gig, and that you are totally at their disposal for making that happen. First among all things you take care of your employees -- they have the worst risk situation of anyone involved.
You will then tell your investors that you're failing and will be proceeding to wind up the business in an orderly fashion. They probably already know this. None of the ones who you care about will hold it against you -- "this is the nature of the business we have chosen." Some of them may likely attempt to invest in your endeavors in the future, if you decide to go down that route.
You will then draw up and execute on a plan to wind down the business in an orderly fashion. Give your customers a window on their apps going dark, if appropriate. Turn off new signups now. Turn off ability to take money now, unless it is absolutely required to continue paying your employees. There likely a small mountain of very boring administrative work here -- your lawyer and accountant can help you through it.
After this is over, you'll probably be very stressed. That is fine and natural. You're in the hottest market ever in terms of hiring right now. If you want a job immediately, you will have many offers for it. "Built a company with real revenues from nothing. Got into an accelerator. Took funding. It didn't work." is enough of a resume to get you an interview at any number of places. If you need introductions, you are probably well-networked enough to get them, but if for some reason you want more drop me an email. Your designer co-founder will have, similarly, no shortage of offers.
Like tptacek says below, this will not meaningfully hurt your chances of creating a business later. You've likely learned plenty through the experience.
It sucks. It will be better, very soon. You don't have to be scared: this is routine and, while it doesn't feel like it, you're actually in very good position, both absolutely and relative to many other people.
The one time so far in the history of Shadowcat I've had to cut people for no reason other than lack of money, I talked to managers I knew at other companies who might have an interest in the sort of talent that I was about to force onto the market.
Two people finished working for me on a friday and started a new job on the following monday. The reduction in stress and guilt and hence increase in my capacity to focus that resulted from knowing that was the outcome for them repaid the time spent finding them new gigs within a handful of days. Maintaining a positive relationship with those people afterwards - and the attitude of people who saw how I'd handled it - was effectively just gravy.
Or: Handling this sort of situation with honour tends to help turn it into a positive sum game.
Having said that, a month to live is still a month to live. Talk about the situation with your team members and advisors and try to figure out whether or not it's salvageable. Perhaps, after making some difficult choices, there's a way that you can still continue. There have been moments in my own startup experience where things seemed really bleak and hopeless, and it seemed time to give up, but in the end we actually got past it. Another friend of mine had a situation where he literally had no money left in the bank and took the company to Vegas on credit card (I don't advise this!), when someone threw him a $200k life preserver at the 11th hour.
I guess the question you really have to ask yourself is whether you still believe in what you're doing. If the answer is no, then I think your involvement with the company has to end, which may or may not be fatal for the startup overall. I feel for you OP - my own startup failed 18 months ago and it's no fun. However, you'll get through it and I hope you decide to try again.
I would add, I usually give myself twenty four hours between drafting and submission of any seriously emotionally charged communications.
sometimes you don't need it, but you want to be as calm (hah) as possible.
Talking to your co-founder "sometime this week" and your employee because if you don't fire him you "fucking won't make payroll" for all of two paychecks should really have been the first moves.
But then, this doesn't sound like someone who cares about much else other than deflecting failure onto his investors and co-founder.
No need to be defensive about it if it did not work out, just go talk to your people.