Or at least he should and since "when the president asks one has to accept" as was said by a previous cross party appointee, so then she should accept.
If Biden sincerely wishes to put country above party and and reach out to even the populist section, and certainly Palin is a significant representative of that large group, then I can't think of a more clear message that he could send in that regard.
Biden appears to have no rancor towards Palin and prior and subsequent to their VP debate he behave in a gentlemanly and honorable manner. Similarly I know of no animus on Palin's part towards him.
Whether Biden has the nous to move in this direction would be a definite and clear signal of a new start.
One can hope.