WASHINGTON  President Obama on Tuesday strongly defended his tax cut deal with Congressional Republicans against intense criticism from his own party, insisting it was “a good deal for the American people.”

Struggling to ensure that the package would win approval, the White House deployed Vice President Joseph R. Biden Jr. to Capitol Hill in a bid to allay the concerns of Senate Democrats. Mr. Obama also held a news conference where, with uncharacteristic emotion, he suggested that liberals were unrealistic about what they could achieve in Washington and also slammed Republicans, at one point comparing them to hostage-takers.

“I’ve said before that I felt that the middle-class tax cuts were being held hostage to the high-end tax cuts,” Mr. Obama said. “I think it’s tempting not to negotiate with hostage-takers, unless the hostage gets harmed. Then people will question the wisdom of that strategy. In this case, the hostage was the American people, and I was not willing to see them get harmed.”

But at the Capitol, Mr. Biden failed to convince many of his old Senate colleagues to line up behind the plan at a tense lunch meeting. In his pitch for support, he called it “a bad situation” but “a good deal,” participants said.