No, it is an adjective. It means "the respect that it deserves".
He walked along the side of a cliff, stepping slowly with due caution=stepping slowly, because a cliff is dangerous and deserves to be treated cautiously.
He spoke to the king with due humility= he spoke humbly to the king, because kings deserve respect.
Your sentence means "the action doesn't deserve much political credit, but it deserves some political credit. However, that credit doesn't belong to [whoever the subject of the sentence is]; the credit belongs to the opposition."