Supreme Court Nominee John Roberts' Frame-of-Reference

Since Article 4, Section 4, of the US Constitution "shall guarantee to every State in this Union a Republican Form of Government"; To whose "Form of Government" is John Roberts, a Harvard graduate, referring when he expresses a "profound appreciation for the role of the court in our constitutional democracy"?

Here is a transcript of a portion of Nominee Roberts' 7/19/2005 acceptance speech from USA Today:

ROBERTS: Thank you, Mr. President. Thank you.

Thank you very much. It is both an honor and very humbling to be nominated to serve on the Supreme Court. Before I became a judge, my law practice consisted largely of arguing cases before the court. That experience left me with a profound appreciation for the role of the court in our constitutional democracy and a deep regard for the court as an institution.