After the bill's passage, Mr. Obama said he hoped the Senate acts with the "same sense of urgency so that it can be one of the first measures I sign into law when I am president."
"In this moment of crisis, ensuring that every child in America has access to affordable health care is not just good economic policy, but a moral obligation we hold as parents and citizens," Mr. Obama said.
The bill, passed by an overwhelming 289 to 139 vote, would increase federal taxes on cigarettes by 61 cents to a dollar a pack to pay the $32.3 billion cost of expanding the State Children's Health Insurance Program for the next 4½ years. Departing President George W. Bush vetoed similar legislation twice in 2007
"Soon we will have a new president who has committed himself to reforming our nation's health care system so every American can access affordable and quality health care." said Rep. Frank Pallone, D-N.J. "The bill we are considering today makes a down-payment on that promise."
About 7 million children from working families with too much income to qualify for Medicaid now get government-sponsored health care.
The Senate Finance Committee is scheduled to begin writing a similar bill Thursday. Some Senate Republicans complain that the House bill expands coverage to include up to 600,000 non-citizen children of legal immigrants.
The Congressional Budget Office projected that nearly 83 percent of the 4.1 million uninsured children who would gain coverage if the bill becomes law are in families with incomes below current eligibility limits. About 700,000 children would gain coverage because their states broadened eligibility.
Republicans also noted that an estimated 2.4 million children currently with private coverage would end up in SCHIP.
They also objected to the additional spending.
"The kids will have to pay through the nose for the things we are doing today," said Rep. Dan Burton, R-Ind. "We don't have the money to do all these things."
"Forty days in Iraq equals over 10 million children in America insured for one year," said House Speaker Nancy Pelosi. "We certainly can afford to do that."
Opponents also said the tobacco tax increase would not be enough to keep pace with the growing costs of health care. As a result, lawmakers down the road will have to cut children from the program or increase taxes. They said the latter option is more likely.
"The Democrats are blowing a giant cloud of smoke into the face of the American taxpayers, and I believe the impending tax increases that must come to cover this program will have us all in a severe coughing fit," said Rep. Dave Camp, R-Mich.
SCHIP was created in 1997 to provide health coverage for children in families that earn too much to qualify for Medicaid, but not enough to afford private insurance. The program was authorized for 10 years. Congress extended the program temporarily through March 31.
The measure passed by the House included a provision that would expand coverage to children of legal immigrants as well as pregnant immigrants.
Current law requires a five-year waiting period before legal immigrants become eligible for coverage under Medicaid and SCHIP. Supporters say expanding coverage would mean children could get treatment for acute conditions like asthma and diabetes so they were less likely to need care in an emergency room.
"These are not illegal immigrants. They are children who go to school, go to daycare with our children, our grandchildren," said Rep. Gene Green R-texas. "Those children ought to have health care."
Passage of the bill follows House votes last week on two labor bills that Democrats also hope to send to the White House in the early days of the Obama administration. One bill reverses a Supreme Court decision that put strict time limits on when a worker can seek redress for pay discrimination and the other specifies that victims of pay discrimination can get compensatory and punitive damages in court.
The Senate is to vote Thursday on taking up the first bill, named for Lilly Ledbetter, a former worker at a tire company factory in Alabama who was denied compensation because she was not aware for years that she was receiving less pay than her male co-workers.