WASHINGTON — Congressional leaders confirmed this week what seemed inevitable with the triumph of Donald J. Trump: The far-reaching trade agreement with 11 other Pacific Rim nations that President Obama hoped to leave as a major legacy, but which Mr. Trump called “a terrible deal,” is dead.

Senator Chuck Schumer of New York, the incoming Democratic leader, told labor leaders on Thursday that the pending Trans-Pacific Partnership, the largest regional trade agreement in history, would not be approved by Congress. Senator Mitch McConnell, Republican of Kentucky and the majority leader, said flat-out “no” when reporters on Wednesday asked whether the agreement would be considered in the lame-duck Congress that convenes next week — its last legislative chance, given the opposition from the president-elect.

Mr. Trump, whose invectives against trade agreements were central to his appeal to disaffected working-class voters, will have the authority as president “to negotiate better deals, as I think he would put it,” Mr. McConnell said.

Yet there is little likelihood of Mr. Trump seeking a new agreement. That reflects not only his campaign statements, but also his yearslong hostility to past trade accords as well as the sheer difficulty of renegotiating a Pacific pact that was seven years in the making, entailing compromises among a dozen countries including Australia, Canada, Chile and Japan, but excluding China.