WASHINGTON — About a week ago, Representative Cedric Richmond of Louisiana, a passionate champion for the poor in New Orleans and the lone Democrat in the state’s congressional delegation, received a phone call from President Obama, pleading for his vote to enhance the president’s trade negotiation powers.

Mr. Obama did not get very far.

“I represent a trade district,” the congressman said. “I could very well vote for this. Problem is, I don’t want to.”

That is a problem for the president. In recent days, he has been personally calling House Democrats, leaning particularly hard on the 45 House members in the Congressional Black Caucus, like Mr. Richmond, whom he hopes in the end can be persuaded to side with him. The pitch is one he has repeated to all audiences: Every modern president but Richard Nixon has had the congressionally given power to negotiate trade deals that cannot be amended or filibustered.

His pro-trade emissary to the caucus, Representative Gregory Meeks, Democrat of New York, makes it more biting: Denying the first African-American president that same authority smacks of bias, especially when opposition is rising in the Republican Party’s Tea Party wing.