The president says he is anxious to sign the bill so those who are still eligible can keep collecting their checks, reports CBS News Correspondent Bob Fuss.
The bill restores federal benefits to more than 750,000 people who were cut off when the program expired Dec. 28 because Congress failed to renew it before adjourning. Another 1.6 million people who exhaust their state benefits would be eligible for federal aid until June 1.
"Today the line is drawn," said Rep. Bill Thomas, R-Calif., chairman of the House Ways and Means Committee, who scolded Democrats who were pushing for even more benefits. "We can do what we should have done back in December."
The Senate already passed the $7.25 billion package Tuesday, opening the first day of a new Congress completely in Republican control.
Passage of the measure helped Republicans avoid a politically damaging issue at a time when the slumping economy is showing no signs of a quick recovery. Democrats and labor unions have loudly blamed the loss of benefits on House Republicans and Mr, Bush, who remained on the sidelines during a legislative stalemate late last year.
"Frankly, it's the least they can do," said House Democratic Leader Nancy Pelosi of California. "But we can do better."
Mr. Bush's late support elevated unemployed workers to the top of the new Congress' must-do list and prodded House Republican leaders to accept largely the same compromise package crafted by Sens. Hillary Rodham Clinton, D-N.Y., and Don Nickles, R-Okla. That plan passed the Senate in November, when it was under Democratic control.
This package was rushed through the halls of Congress at a speed not normally seen in the opening days of a new session.
"I believe this is the right thing to do," said Thomas, who supported a more modest proposal passed by the House last year that would have extended the 13-weeks of federal benefits only to workers in a few high unemployment states. "It is absolutely essential that we do it today rather than argue," he said.
House Speaker Dennis Hastert, R-Ill., said Wednesday it would be "continuation of a very generous program," brushing off Democratic claims that the package was inadequate.
"Nothing is good enough for them," said House Majority Leader Tom DeLay, R-Texas, saying Democrats would extend benefits indefinitely "so someone could stay out of work for the rest of their lives."
The nation's unemployment rate has soared to match an eight-year high of 6 percent in November. December's figures will be released Friday by the Labor Department.
House Republicans favored tax cuts to stimulate economic growth, saying that would help jobless workers more than Democrats' attempts to expand jobless benefits. Four Republicans voted against the benefits extension.
Democrats questioned House GOP leaders' late support for a larger unemployment package. They also accused the White House of neglecting unemployed workers until Mr. Bush could reap political benefits.
Rep. Jim McDermott, D-Wash., said he thinks the White House wants to boast about extending jobless benefits in a show of concern for the downtrodden while at the same time unveiling a stimulus package that benefits wealthy Americans.
"If you're going to stab people, first you've got to give them a ham sandwich," McDermott said.
Mr. Bush was in Chicago Tuesday introducing his "growth and jobs" economic stimulus plan at the same time the Senate was nearing passage of the unemployment benefits. Mr. Bush's plan would provide tax relief to an estimated 92 million Americans by accelerating income tax rate cuts, wiping out all federal taxes on stock dividends paid to investors and boosting the child tax credit by $400 per child.