And even if they didn't have the cash on hand, they could probably get a bridge loan against the expected donations provided they can provide proof that the "the money is on the way".
This is called factoring and is common in corporate finance where Y net-N (payment after N days or Y% discount at 10 days) is standard operating procedure.
The Red Cross would sell their invoices from the telephone companies at a discount to a third party. Although, the possibility of fraudulent contributions may complicate this plan.
