When the Senate Finance Committee votes Wednesday on its sweeping health care reform bill, Senate Majority Leader Harry Reid will face a daunting task: merging two Senate bills into one -- and presumably one that includes a government-run insurance plan that he and other liberal Democrats have steadfastly backed.

The pivotal Senate committee voted last week to strike two amendments that would establish a so-called public option to compete with private insurance coverage. The committee is awaiting a report on cost projections from the Congressional Budget Office before it votes on the legislation, which does not contain a government-run health insurance plan or require employers to offer insurance to their employees.

But the bill created in July by the Senate Committee on Health, Education, Labor, and Pensions includes the two fundamental provisions that the finance committee legislation does not -- and Reid will be forced to meld the two bills into one for the full Senate to consider as early as Oct. 12.

The question over whether Reid will push for a government-run insurance plan in the final legislation remains to be answered. The Senate Majority Leader has said a public option is essential to reform, and other leading Democrats like House Speaker Nancy Pelosi have stressed its importance in expanding coverage to the millions of uninsured.

"We are going to have a public option before this bill goes to the president's desk," Reid said in a conference call with constituents last Thursday. "I believe the public option is so vitally important to create a level playing field and prevent the insurance companies from taking advantage of us."

For Democrats to acquire the 60 votes needed to overcome a Republican filibuster, the final bill must win the support of every Democrat and Independent in the Senate, including Democrats like Sens. Ron Wyden, D-Ore., and Jay Rockefeller, D-W.Va., who on Sunday remained undecided over the finance committee's legislation.

Congressional aides tell FOX News that Reid will work closely with Senate Finance Committee chairman Max Baucus, D-Mont., as well as Health committee chairman Tom Harkin, D-Iowa, in blending the two bills into one that can win in the Senate -- and withstand defeat when the two Houses vote later this year.

White House press secretary Robert Gibbs said Monday that President Obama is focused on a health care reform bill that "ensures choice and competition," but stopped short of saying whether the sweeping overhaul would include a so-called public plan -- despite widespread reports that administration officials are engaged in closed-door meetings with Democratic lawmakers to push for its passage.

Obama hosted a meeting of 150 physicians from all 50 states in the Rose Garden of the White House on Monday to speak about the urgency of health care reform. Among the groups heavily represented was Doctors for America, a grassroots organization that backs a government-run insurance option.

In a recent survey published in the New England Journal of Medicine, roughly 63 percent of U.S. physicians favor a public option to compete with private insurance plans.

"Doctors appear to think that Medicare does a pretty good job," said Dr. Alex Federman, a general internist at Mt. Sinai Medical Center in New York, who along with another physician conducted the survey. "The extrapolation of that is that if you have a public insurer in the mix, you're going to have some assurance that patients will get the care that they need."

Rockefeller and others have said they intend to fight for the public option on the Senate floor or in later negotiations with the House. The current House version of the bill includes a government-run to compete with private insurers. The American Medical Association, which had previously said insurance should be expanded only through private insurers, has endorsed the House version of the bill.