Conway is best known nationally for losing to GOP Senator Rand Paul in 2010 for the Kentucky Senate seat vacated by Republican Hall of Fame pitcher Jim Bunning.
Early Tuesday, the former president's body was carried from the Capitol Rotunda, where he lay in state for three days, and brought down a marble hall by military pallbearers to lie outside theSenate chamber.
New York's mayor, Michael Bloomberg, a liberal Republican, pointed out last week at a Senate town-hall hearing in Philadelphia that the Big Apple's economy would collapse without the half-million or so undocumented people among the city's 3m immigrants.