Instead of embracing one-on-one talks with Boehner, he is trying to win over a wider range of lawmakers, particularly in the Senate, where White House officials think having broad support gives them the best chance of getting a proposal through the Republican-controlled House.

Sen. Mary Landrieu (D-La.) said the dinners and conversations the president has initiated are aimed at sketching out the possible parameters for a broad budget agreement rather than pressuring lawmakers. “This is not a lobbying drive that he’s waging,” she said.

White House officials and many of Obama’s allies question whether the personal-touch politics and horse-trading that greased legislation in the past can work today. Referring to former president Johnson’s famous dealmaking tactics, Daley said that these days, “you’d go to jail for what Johnson did.”

“How would you cover a story that Obama gave Senator X a military base or kept it open for a vote for gun control?” he asked. “You’d massacre them. You’d call for impeachment.”

Rep. Chris Van Hollen (D-Md.) said the challenge facing Obama is that he needs the support of a group of lawmakers unresponsive to broad public opinion and uninterested in political trades.