Yeah. That's a pretty lousy excuse for not wanting to invest in some more processing power.
I know that, to scale your web functionality to the maximum of your customer base is a ridiculous notion, but you might want to make sure that you have baseline plus a comfortable margin at all times, and emergency supplemental capacity when the demand balloons.
I'm sure there are plenty of companies that are willing to help, it's just a question of writing a check . . Oh, right.