Rep. Charles Rangel, the incoming chairman of a powerful House tax committee after the Democrats election wins, vowed yesterday to work with past GOP foes even as he aimed to take key office space away from his old nemesis, Vice President Cheney.

Mr. Rangel was one of many New Yorkers who saw the national outcome propel them up the ladder of political power, or send them tumbling. “It’s going to be a new day,” said Mr. Rangel, the longtime congressman who will soon lead the Ways & Means committee, said at his Harlem office.

“We Democrats have to prove that we deserve to be a part of the leadership,” Mr. Rangel said. “The president’s going to have to decide whether he wants to be a lame duck president.”

But Mr. Rangel was quick to take a shot at Mr. Cheney, his longtime political foe. The congressman noted that Mr. Cheney has been keeping an office on the second floor of the House of Representatives, space historically used by the Ways & Means chairman. Laughing, Mr. Rangel said: “I’m trying to find some way to be gentle to restore the dignity of that office.”

In the heat of the campaign season, Mr. Rangel erupted when Mr. Cheney said the congressman didn’t understand how the economy worked. The two have exchanged verbal fire for more than a year.

Yet even as he sounded an early conciliatory note to Republicans, Mr. Rangel couldn’t resist hurling at least one more volley.

Asked about an immigration reform package that was pushed this year by President Bush and some Democrats, Mr. Rangel said a law creating a category of immigrant guest workers would be “as close to slavery as you can legally get.”