Looking at their most recent Form 990, the American Red Cross has over a billion dollars in liquid cash/savings, with another 1.5 billion in more fixed assets, and cash flow of over 3 billion.
90 days is nothing. Agitating for clearing the funds faster is just going to add overhead.
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.
You're correct, the breakdown for a monthly SMS fee is $500-$1,000 (for a 'vanity' short code) just to hand on to the name (think of it as paying $500 for a domain name of a random sequence of characters or $1000 for a domain of your choosing).
It doesn't stop there thought. Typically you have to pay an aggregator to send and receive messages from the cell networks. This usually costs thousands of dollars and is broken down between a monthly fixed cost or a cost per message (typically $0.04-$0.05 per outgoing message or $0.01 per incoming message).
But that's not for fund raising short codes. If you're a corporation, the cellphone companies take anywhere from 50%-75% of the amount that is to be billed to the customer; however, this number is much lower for non-profits. The caveat though is that not many non-profit organizations are approved for these lower rates; companies like mGive and MobileCause have to do a lot of work to get this clearance from cellular phone companies and act as an aggregator for non-profits.
Oh, and there's one more thing: the application process, which is a fucking nightmare. It takes 3-6 months to get a non-charging short code and thousands of dollars without any guarantee of approval. Worse yet, each cellular network has to approve of your application so if all US cellphone companies approve, but one like Verizon says, "No, sorry," you're screwed. When our company went through this process, one cell provider said, "No," at first, and then asked us for a sample of the SMS messages that we would send and receive.
Net net: its a fucking mess out there in the SMS short code world. If you want to see what a world of non-net-netruality looks like, look no further than cellular providers.
Even if you don't have assets and flow to cover it... That's what http://en.m.wikipedia.org/wiki/Factoring_(finance) is for and surely there's a company out there that'd do it for free / for publicity.
http://ConvoyofHope.org is a highly rated charity with a warehouse in Haiti and people on the ground. A web donation is still pretty convenient, so if your looking to put your money to work ASAP, look them up.
But, knowing the money is coming is enough for lots of relief-related spending to occur: drawing down existing balances below usual levels, putting supply/travel purchases on credit, etc.
Even if actual cash is required, a 90-day loan backed by the certainty of mobile payments clearing should be dirt cheap, too. So this delay may not make much of a practical difference.
90 days is nothing. Agitating for clearing the funds faster is just going to add overhead.