Now that I've stopped laughing at so many things stated in this piece, (none of my thoughts are relevant) I'd like to say that I've never heard this phrase worded quite this way.
I really did have to read it in context to figure it out for sure.
I'm familiar with "cheap at that price" but not "the price."
Even then, I think it's awkwardly worded.
I'd more readily expect it to be written:
Chelsea Clinton's wedding will cost $3 million, but even at that price, it's still cheap.
(meaning: considering whose wedding it is.)
Also, I think the word cheap as used here is kind of insulting because I think of cheap as tacky and unclassy because they didn't want to spend the money to make it an admirable affair.
A more understandable phrase in AE would have been a modest amount.