The Ashcroft campaign says Mr Carnahan is a raging socialist, guilty of campaign-finance scandals and soft on crime (he once agreed to the pope's request to commutea death sentence).
His family filed a petition for clemency to commute the 20-year sentence, a request that was denied by President George W. Bush in one of his final acts in office.
Mr Straw's most recent intervention was on 30 January when he contacted the chairman of the Texas Board of Pardons and Parole to urge them to commute the death sentence to a prison term and reiterate Britain's opposition to capital punishment.