There are other executive positions besides President and VP. FDR got his as Assistant Secretary of the Navy. Others have served in cabinet positions (Secretary of State is often one). Eisenhower was military (still federal and executive). But it is more about EXECUTIVE experience than "federal" experience. Many with Federal POLITICAL experience have run (Senators and Congressmen), but not many have succeeded. State governors have often been tapped.
Then again, maybe you should. It is alot of what we are fighting right now.