The political thing to do, or the honorable thing to do? Look at the sitting president. Got elected to the Senate, and almost immediately made running for prez his full time job, but he did occasionally find time to jet back to DC and vote against Freedom whenever the need arose. He liked to blame others for the Patriot Act, but we all know he would have voted for it if he were in Congress at the time.
During the primary debates it became clear to everybody who paid any attention that he was the most useless member of the Senate since Carol's Mossy Bum, but it didn't seem to hurt his election hopes any. (CMB was from Chicago also. Coincidence?) http://en.wikipedia.org/wiki/Carol_Moseley_Braun
IMO, it's easier to get elected to public office when you're currently holding public office. The fact that you aren't devoting yourself to the last job you were elected to do doesn't seem to bother the voters much.