WASHINGTON (AP) — Victory within reach, President Barack Obama exhorted House Democrats on Saturday to stay true to their party’s legacy and make history by bringing health insurance to millions of struggling families now left out. Leaders exuded confidence as they defused thorny problems in the countdown to a landmark vote.

Obama evoked Abraham Lincoln’s moral compass and extolled Democratic achievements such as Social Security and Medicare — once controversial, now an essential part of the social fabric — on a day marked by a frenetic hunt for votes inside the Capitol and angry t...