WASHINGTON: President Barack Obama has signed into law a sweeping overhaul of US health care in a defining moment of his presidency, but one last chapter in the epic struggle is still playing out in the Senate.

Senators are debating a package of fixes to the new health reform law, demanded by House Democrats as their price for passing the nearly $1 trillion overhaul legislation that will extend coverage to 32 million uninsured Americans over the next decade.

Obama signed the bill on Tuesday, declaring "a new season in America" as he sealed a victory denied to a line of presidents stretching back nearly half a century. Failure would have weakened him and endangered other issues on the president's ambitious domestic agenda, including immigration reform and climate change legislation.

The fix-it bill under consideration in the Senate eliminates special deals for some individual states from the new law, softens a tax on high-cost insurance plans that was repugnant to organised labour, provides more expansive subsidies to lower-income people to purchase insurance, and offers more generous prescription drug coverage to seniors, among other changes.

Its approval at the end of this week is virtually assured, since it's being debated under fast-track budget rules that allow passage with a simple majority instead of the 60 votes usually required for action in the 100-seat Senate. Democrats control 59 Senate seats.

That didn't stop Republicans, who are unanimously opposed, from using the floor debate that began on Tuesday afternoon in the Senate as an opportunity to repeat the accusations they have lobbed at Obama's health legislation for the past year: that it raises taxes, slashes Medicare coverage for seniors, and includes a burdensome and constitutionally questionable requirement for nearly all Americans to carry health insurance.

The Republicans came up with some new arguments too, including an amendment offered by Sen Tom Coburn that would prohibit sex offenders from getting Viagra prescriptions under federal health programmes.

Democratic Sen Dick Durbin dismissed that as a "gotcha amendment" designed to be difficult for Democrats to oppose.

The main suspense surrounding this week's debate is whether the fix-it bill can emerge from the Senate unchanged. If it does, it can go straight to the president for his signature, since it's already passed the House of Representatives.

If there are only minor changes the House would be almost certain to pass the bill again with little trouble, but if Republicans succeed in knocking out a significant provision or attaching a substantive amendment there could be difficulties in the House, where the legislation passed very narrowly Sunday night.

Democratic leaders in the House and Senate say they have scrubbed the fix-it bill thoroughly to ensure that will not happen.