As soon as you get a factoring company involved you immediately lose a % of your income - can your business model afford that in the longer term ? A short term overdraft might actually work out cheaper in the long run
Before going down that route you need to make sure you've got effective credit management procedures in place - statement after 30 days, letter 7 days after that followed by phone calls asking for payment and then letters threatening legal proceedings. If you haven't got the time then have you thought about employing a temp for a day or even half a day to do the ringing round ? If your business is new you might not have experience at chasing debts - it can be a stressful process and you need to devote some time to it but it can be done.
The other obvious option is to delay paying your suppliers (never pay before the end of their credit period and if in real difficulty delay until they ring up chasing or send a really stroppy letter) and also to take as little money out of the business yourself as possible until the cashflow has improved. I know this doesn't help other businesses out but if it gets you through a short term problem then so be it.
If the majority of your costs can't be deferred (wages and rent) then you probably need to think about the terms you are offering your customers - maybe only offer them 14 days to pay before starting recovery procedures. The idea of charging them interest after a given period of time is also a good one and you could also offer a discount for prompt payment (which over time you could factor into your pricing structure).
Good luck.