This is a good question to show the distinctions among different types of nonprofit organizations.  (See Ready Reference Page:  “What Do We Mean When We Say ‘Nonprofit’?”) The answer depends on the tax status of the “nonprofit” involved.  Only if the organization is a 501(c)(3) charity is there likely to be a significant limit on its activity in this regard.  501(c)(4) social welfare organizations or 501(c)(6) trade associations do not face the same limitations on their political activity and can basically support or oppose nominees as much as they want.

A 501(c)(3) charity is effectively prohibited from endorsing or opposing a candidate for a public office, but the IRS concluded that attempting to influence the Senate confirmation of a federal judicial nominee does not constitute participation or intervention in a political campaign. (Notice 88-76)  

The IRS has concluded that attempting to influence Senate confirmation is “lobbying,” which a 501(c)(3) public charity is permitted to do so long as it is not a substantial part of its activities.  Although the Notice deals only with judicial appointments (and was particularly relevant to Supreme Court appointments at the time), the rationale is the same in dealing with any position requiring the advice and consent of the Senate.  “The Senate’s confirmation vote constitutes a vote on legislation” for purpose of this analysis, the Notice says.  Therefore, a public charity should not be afraid to voice its opinion for or against a Cabinet nominee or other person whose appointment must be confirmed by the Senate.  The organization just needs to be sure that it is not a substantial part of its activities or is within the expenditure limits of section 501(h).

A 501(c)(3) private foundation is generally not permitted to lobby in its own name and its direct involvement in seeking to influence Senate confirmation would constitute a taxable expenditure subject to an excise tax.