A high-stakes U.S.-Russian plan for destroying Syria's chemical weapons is in jeopardy on several fronts, with the regime in Damascus facing growing allegations that it violated the agreement by attacking rebels and civilians with chlorine gas.

Despite the allegations of new chemical attacks, there is no indication the U.S. is considering reviving its threat of military strikes. National Security Adviser Susan Rice on Wednesday emphasized the plan's achievements in eradicating the vast majority of the weapons, saying even...