WASHINGTON — As their leaders inch toward agreeing to higher tax rates, dozens of House Republicans find themselves caught between the will of a larger American public that favors higher taxes on the rich and the wishes of constituents who re-elected them overwhelmingly to oppose the Obama agenda at every turn.

With the last House race decided over the weekend, the conflict between a Democratic president convincingly re-elected to a second term and the House Republicans who held their majority illustrates a striking dichotomy in the nation’s body politic: the president and a majority of senators, including a growing number of Republicans, back compromise on tax rates and say the public is on their side, and a majority of the House, in artfully drawn districts, claim just the opposite.

“We ran aggressively talking about taxes and growth and spending, as did the president,” said Representative Sean P. Duffy, a first-term Republican from Wisconsin, who despite being a top target of Democrats easily won re-election by 12 percentage points. “The president keeps talking about his mandate. Well, he doesn’t have a mandate in the Seventh District.”

Given the electoral dynamics, the lawmakers who are broaching the possibility of raising tax rates as a way to strike a deal and prevent the possibility of a recession are beginning to appeal to House members with a term not heard often in the House — the national interest.