While Obama is buoyed on the question by a high, 79 percent approval rating from Democrats, Boehner is saddled with a basically even verdict from GOP voters (39 percent approve, 37 percent disapprove) thanks to divisions within the congressional delegation he leads.

Boehner has struggled to maintain party discipline among the most conservative congressional Republicans, many who rode the tea party wave into office in 2010. But in the poll, Boehner is weakest in the ideological middle. Nearly half of “very conservative” Republicans and independents (49 percent) approve of how Boehner is handling the negotiations, but that number drops to 35 percent among those who are “somewhat conservative” and further still — to 23 percent — among self-described “moderates.”