NO. Not if their actions are because they are negligent or incompetant. It’s affirmative only if the duties of their office are in question, not if their own actions are in question. If their personal actions are in question, they must pay their own way.
IMO It is not the duties of their office, but their own lack of action that is being challenged; therefore, they should provide their own personal counsel.
Ask yourself, what are the duties of the office and did they fulfill that duty?
How do they even have an obligation under the law to take action if it is not as a duty of their offices? Hillary Clinton, private citizen, has no legal obligation to take action regarding Obama's eligibility. Same for Gates. Same for Biden.