WASHINGTON—Democrats are edging closer to giving President Barack Obama a big victory on health care.

The Senate was expected to vote Thursday on legislation that would spend $31.5 billion more on a children's health insurance program over the next 4 1/2 years. The additional money would help about 4 million uninsured children get coverage and draw 2.4 million more kids into the program who otherwise could get private coverage.

"It's a major step forward for our nation," said Sen. Jeff Bingaman, D-N.M., in anticipation of the Senate's action. "Many Americans face grave economic uncertainty, and it's critical that we move quickly to pass this legislation and send it to President Obama for his signature."

So far, the debate this week has given Democrats a chance to wield their expanded majority, batting down all the GOP attempts to change the bill.

Democrats want to pay for expanding the State Children's Health Insurance Program by increasing the federal excise tax on cigarettes by 61 cents per pack, to $1 from 39 cents currently.

Republicans have countered with a more modest proposal that they said would expand coverage to about 2 million uninsured children. Their proposal, offered Wednesday by Senate GOP leader Mitch McConnell of Kentucky, would have increased spending on children's health coverage by about $10 billion over the next 4 1/2 years.

That plan would have lowered spending for certain Medicaid services, particularly the amount paid to states for administrative tasks associated with managing Medicaid, but the amendment was soundly defeated.

Republicans say they are most concerned about a lack of firm income limits on who can get the government to pay for their children's health coverage. States have broad flexibility to determine eligibility criteria. Republicans say some states have veered from the program's original intent to serve the working poor.

The House bill won approval two weeks ago.