WASHINGTON — After he left Wall Street to enter politics eight years ago, Representative Jim Himes, Democrat of Connecticut, began fielding the occasional question of when he intended to run for president. “It has come up in jest any number of times,†said Mr. Himes, who always has his answer ready. “There could be constitutional questions.†Mr. Himes, you see, was born in Peru in 1966 while his father worked for the Ford Foundation. That makes him one of at least 17 current members of Congress who, because of their birth outside the United States, could run afoul of the...