Your escrow is money earmarked for upcoming tax and/or insurance payments, so they'll pay out of that amount first. Your escrow account could end up negative if it contains too little to cover the bill. Technically speaking they *could* ask you to immediately cover any deficiency. More often than not, they simply adjust your payment amount to allow for them to recover the deficiency and to have enough to cover your next payments.
It's really no big deal, and usually just sorts itself out. They'll send you a letter about your new payment amount, and how they calculated, and you'll begin paying that amount as of a given date.