In many states, eligibility expansions have passed with solid bipartisan support. In one of her final acts as governor of Kansas in April, Ms. Sebelius, a Democrat, signed a two-year expansion worth $4.4 million that had been approved by her overwhelmingly Republican Legislature.

The broadening of eligibility has made a profound difference for parents like Vicky and Dewayne McIntyre of Yakima, Wash. When their state lifted the income cutoff for its program to 300 percent of the federal poverty level (or $54,930 for their family of three) from 250 percent (or $45,775), the McIntyres learned that their 8-year-old daughter, Sarah, had become eligible for the first time.

Sarah, who endured lung surgery at 3 and heart surgery at 6 and now has asthma, had been uninsured for a year. “We were into credit card debt and payday loans,” said Ms. McIntyre, 41, who works part time in a store to supplement her husband’s income as a welder. “Her medicine at one point was $880 a month, and we had to pay cash, so we were struggling. It is such a relief now that I can just take her to the doctor if I need to and get her medicine.”

The federal legislation, which extended the program through 2013, provided $32.8 billion in new financing over that period, paid with an increase in tobacco taxes. On the day Mr. Obama signed the bill, calling it a “down payment” on universal coverage, he also rescinded a Bush administration directive that effectively made it impossible for states to raise their eligibility limits above 250 percent of the poverty level.

The new law allows states to provide coverage to children from families living at up to three times the poverty level. States can set thresholds higher if they wish, but will be reimbursed by the federal government at a lower rate  the same paid for Medicaid recipients. A primary incentive for states to expand coverage is that Washington, on average, pays 70 percent of the cost of CHIP, compared with only 57 percent for Medicaid.

Some states, including New York and New Jersey, were already enrolling children above three times the poverty level, but the federal legislation and the rescinding of the Bush directive made it possible for about 40 states to broaden eligibility.

The reauthorization of CHIP concluded a bruising two-year political battle. President George W. Bush twice vetoed Democratic measures to expand the program in 2007, depicting the legislation as a stalking horse for government-run health care. Congressional Democrats sustained it through temporary extensions and took full political advantage of Mr. Bush’s stance during the 2008 campaign.