The fate of a government-run health insurance plan may rest in President Obama's hands after the Senate Finance Committee rejected amendments that would include the so-called "public option" in its version of health care reform legislation.

Liberal Democrats failed twice on Tuesday to include a government-run insurance option in the legislation before the committee, the last of five congressional panels completing work on the president's top domestic priority. 

Once touted by Obama as essential in "keeping insurance companies honest," the government plan was blasted by Senate Republicans and moderate Democrats, some of whom argued it would lead to a single-payer system.

The vote to strike down two separate amendments underscored the disagreement among Democrats over the necessity of a public option. Whether Obama will continue to fight for it remains to be seen.

The first amendment, proposed by Sen. John D. Rockefeller of West Virginia, was rejected 15 to 8. The second, penned by Senator Chuck Schumer of New York, was defeated 13 to 10. 

Rockefeller had proposed a plan modeled on Medicare, the federal health care program for senior citizens, in which the government would set what it pays doctors, hospitals and other medical providers. Schumer proposed a government plan that would look more like a private insurance company and negotiate payment rates with providers.

Sen. John Ensign, D-NV, was quick to pounce on Rockefeller's amendment, arguing that his idea for a public option would deny doctors participation in Medicare for two years if they choose not to participate in a new government program.  

Others, including Sen. Kent Conrad, D-ND, who has crafted an alternative plan that would set up a series of non-profit health care cooperatives, blasted Rockefeller's plan, saying, "The devil is in the details." He said if the amendment is implemented, "every major hospital goes broke."

The White House has been backtracking on its commitment to a public option. Obama made "universal health care" a centerpiece of his presidential campaign, but he later said a government-run program was not essential to reform.

"The public option, whether we have it or we don't have it, is not the entirety of health care reform," the president said at a town hall meeting in Colorado on Aug. 15. "This is just one sliver of it, one aspect of it."

Health Secretary Kathleen Sebelius has said that the public option "is not the essential element" and has suggested that non-profit cooperatives would be a viable alternative. 

Supporters of a government-run plan have 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.

House Speaker Nancy Pelosi, a strong supporter of a government plan, said Tuesday there's no rush on passing a House bill, especially since the legislation won't take effect until 2013.

"I believe we will have a public option in our bill," Pelosi said during a briefing Tuesday with reporters.

But senior Senate Democratic aides told FOX News that Majority Leader Harry Reid, D-NV, will not include a public option in a health care reform bill he will create once the Finance Committee completes its action this week.

After shooting down the two amendments, the committee will reconvene Wednesday to debate a number of other important issues in health care legislation, including thorny issues like abortion and insurance coverage for illegal immigrants.

FOX News' Trish Turner and the Associated Press contributed to this report.