WASHINGTON — A leading Senate Democrat said today his party is determined to push through a health care overhaul bill with or without Republican support because the “system is broken.”

“We prefer to go at it with Republicans if we can reach compromises in some areas,” said Sen. Charles Schumer, D-N.Y. “But we’re not going to not pass a bill.”

Schumer dueled with Republican Sen. Kay Bailey Hutchison on a network morning news show in the wake of a key Senate vote Saturday night that advanced a 10-year, $959 billion health bill to full debate. Hutchison argued that “you’re going to put taxes and mandates on business” that would be a drag on an economy still struggling to recover from recession.

Congressional Democrats are trying to resolve differences within their rank and file over abortion, taxes and letting the government sell health insurance as a competitor with private insurers. Those are all crucial policy questions, and House and Senate Democrats have taken conflicting approaches.

Appearing on NBC’s “Today” show this morning, Schumer said, “We all know we have to give a little. ... If we don’t do anything, that is the worst situation, and we have a good bill.” He said lawmakers must come together because “the health care system is broken.”

Schumer argued that Republican critics “haven’t put any alternative on the floor.”

Hutchison called it “a terrible idea at this time.” She said that Republicans “have put alternatives on the floor,” including individual tax credits that would not include cutting Medicare and permitting a government takeover of the health care system.

Hutchison is challenging incumbent Republican Rick Perry for Texas’ governorship and is a near certain vote against any Democratic health care plan. However, Senate leaders hope to persuade moderate Sen. Olympia Snowe, R-Maine, who voted for a Democratic bill in the Finance Committee, to back final legislation.

The Democratic measures would leave 12 million or more eligible Americans uninsured. Many middle-class families who’d now be required to buy coverage would still find the premiums a stretch, even with government aid. A new federal fund to provide temporary coverage for people with health problems would quickly run out of cash.

For now, these bread-and-butter concerns take a back seat to more pressing issues for Democratic lawmakers trying to deliver on President Barack Obama’s signature issue.

The House passed its health care bill 220-215 earlier this month. The Senate cleared the way Saturday for debate on legislation unveiled by Majority Leader Harry Reid, D-Nev. The bill, a compromise between two committee-passed versions, could undergo significant changes as senators amend it during weeks of arduous debate ahead.

Both bills would require all Americans to carry health insurance, with government help to make premiums more affordable. They would ban insurance companies from denying coverage or charging more to people with health problems. They would set up new insurance markets for those who now have the hardest time finding and keeping coverage — self-employed people and small businesses. Americans insured through big employer plans would gain new consumer protections but wouldn’t face major changes. Seniors would get better prescription coverage.

“For the first time, we’re going to allow American consumers to be involved in a buyers’ market for health insurance,” said Sen. Chris Dodd, D-Conn., one of the authors of the Senate bill. “This Congress is going to pass, and this president is going to sign, a national health care program for all Americans.”

Before any signing ceremony, lawmakers must clear some tall hurdles.

On abortion funding, the House adopted strict limitations as the price for getting anti-abortion Democrats to vote for the final bill. Abortion rights supporters are backing Reid’s approach in the Senate bill, which tries to preserve coverage for abortion while stipulating that federal dollars may not be used except in cases of rape, incest, or to save the life of the mother.

In the end, Reid may have to bend. Catholic bishops say they can’t accept his approach because it would let federally subsidized plans cover abortion. They vow to oppose the health care bill unless, like the House, the Senate enacts stronger language. Democratic senators opposed to abortion are already threatening a battle.

On financing, the House relies mainly on an income tax hike for upper-earners to pay for expanded coverage. The Senate opted for a tax on high-cost insurance plans, a Medicare payroll tax hike on the wealthy and fees on medical industries. In polls, the House approach is more popular. The Obama administration has signaled it likes the Senate’s insurance tax.

That leaves the controversy over a creating a government health plan to compete with the insurance industry. It has dominated the debate and remains unresolved.

Both House and Senate bills now provide for a government insurance plan, but Reid’s bill would let states opt out. It’s not clear that Reid has the votes. He may be able to get a compromise to allow a government plan only if, after a reasonable time, insurance companies fail to deliver lower premiums.

Resolving these policy issues would be a historic accomplishment for Democrats. But the bill could still leave consumers feeling a little cheated.