WASHINGTON -- A sweeping health overhaul bill has survived a major challenge from the left, but onslaughts loom from the right on thorny issues including abortion and insurance coverage for illegal immigrants.

Liberal Democrats failed in two efforts Tuesday to include a government-run insurance option in the legislation before the Senate Finance Committee. Finance is the last of five congressional panels completing work on President Barack Obama's No. 1 domestic priority, a top-to-bottom reshaping of the U.S. health care system to hold down costs and extend coverage to the uninsured.

The outcome was expected in the moderate committee, which is the only of the five not to have embraced an new federally-run insurance plan that would compete with private insurers. Advocates say the competition would help consumers while opponents say it would destroy private companies and result in a government takeover of health care.

The committee's chairman, Sen. Max Baucus, D-Mont., said he saw features to like in the so-called public plan but that it wouldn't get the 60 votes necessary to advance in the Senate. "My first job is to get this bill across the finish line," said Baucus, who'd proposed nonprofit, member-owned cooperatives instead.

Supporters of the so-called "public option" vowed to keep up their fight as the bill moves toward the Senate floor, and then to negotiations with the House. Democratic leaders in both chambers are pushing for floor votes in the fall.

"We are going to keep at this and at this and at this until we succeed because we believe in it so strongly," said Sen. Charles Schumer, D-N.Y.

But first the bill has to get out of the Finance Committee, where hurdles will greet senators as they reconvene Wednesday for their sixth day of work. Among them: amendments expected to be offered by minority Republicans to strengthen prohibitions against illegal immigrants getting federal funding to buy insurance.

Also pending are amendments to ensure there is no federal funding for abortion.

Baucus has already tightened up language in his bill on both those issues, but they are highly fraught and critics see loopholes they want to close.

Those issues are also still pending in the House, where Democratic leaders hope to finalize legislation this week that would merge the work of three separate committees into one. Speaker Nancy Pelosi, D-Calif., was to meet with the full Democratic caucus Wednesday morning to discuss issues including the final shape of a public plan she intends to include in the House bill, and how to pare the bill down to $900 billion over 10 years -- Obama's preferred price tag and about how much the Senate Finance version costs.

In the Finance Committee, a public plan amendment offered by Sen. Jay Rockefeller, D-W.Va., failed 15 to 8, with Baucus and four other committee Democrats joining all 10 Republicans to vote no. A moderated version by Schumer went down 13-10.

It's possible that the committee could take up the public plan issue again in the form of one or more compromises being debated among senators. One of those comes from Sen. Olympia Snowe of Maine, the only Republican viewed as a possible "yes" vote on the final bill.

Snowe has proposed a public plan that would go into effect only in states where private companies weren't offering affordable enough alternatives. She said late Tuesday that she was discussing the so-called "trigger" compromise with committee Democrats and hadn't decided how to proceed.

The public plan votes were the highlight Tuesday as the panel pushed forward with legislation that generally adheres to conditions that Obama has called for. The bill includes new consumer protections, including a ban on companies denying insurance on the basis of pre-existing conditions. At the same time it provides government subsidies to help lower-income Americans afford insurance that is currently beyond their means. It also includes steps that supporters say will begin to slow the growth in health care costs nationwide.

In addition to the public option amendments, the committee agreed late Tuesday to a measure that would require lawmakers to shop for insurance within new state purchasing exchanges the bill would set up. The measure's author, Sen. Charles Grassley, R-Iowa, said it was only fair that if their constituents had to enter the exchanges, lawmakers should too.

The committee defeated an amendment, also by Grassley, that would have allowed states to opt out of a new requirement for every individual to purchase insurance coverage or pay a fine.