Akin has to withdraw quickly in order to get the Courts to approve the substitution. Sufficient public pressure will be put on Carnahan and others to approve the switch.
However, if he delays, then the courts and Carnahan will be a lot less friendly — and get away with it.
If in fact Akin does petition court, and Carnahan does not unnecessarily delay her (and others) decision the state central cmte. of the MO Republican Party would have 28 days or until Oct. 12 (whichever comes first) to name a replacement. But Carnahan/Dems could conceivably drag this out. Prolong the agony. She is not standing for re election so public opinion matters little to her.