Hillary Clinton and her Democratic allies, unnerved by the tightening presidential race, are making a major push to dissuade disaffected voters from backing third-party candidates, and pouring more energy into Rust Belt states, where Donald J. Trump is gaining ground. With Clinton enduring one of the rockiest stretches of her second bid for the presidency, her campaign and affiliated Democratic groups are shifting their focus to those voters, many of them millennials, who recoil at Trump, her Republican opponent, but now favor the Libertarian nominee, Gary Johnson, or the Green Party candidate, Jill Stein. While still optimistic that the race will turn decisively back in Mrs. Clinton’s favor after the debates, leading Democrats have been alarmed by the drift of young voters toward the third-party candidates.