Despite months of claims by politicians and political observers that a public health care option couldn't pass the Senate, multiple news sources reported Thursday that a government-run public health insurance plan is back on the Senate agenda.

Senate Majority Leader Harry Reid (D-NV) is said to be "leaning towards" including a public option in the bill that will hit the Senate floor in the coming weeks. The Senate Finance Committee -- whose support is crucial to any bill having to do with government spending -- head earlier approved a version of health care reform without the public option.

The conventional wisdom about the public option's chances has changed little in recent weeks -- there aren't the 60 votes necessary in the Senate to defeat a Republican filibuster of the bill.

But, as ABC's Jonathan Karl reports, Reid reportedly believes he could convince some conservative Democratic Senators to vote down the GOP filibuster, but still vote against the bill itself. The public option would then require only 51 votes to pass, and it appears that level of support does exist.

The form of public health insurance Reid and other Senate leaders are considering would include an "opt-out" clause that would allow individual states not to participate in the plan if they so choose, according to a report at Roll Call.

BAUCUS 'WENT TO DEFCON 1' OVER PUBLIC OPTION IDEA

"If Senate Majority Leader Harry Reid and the White House included a public option in the Senate bill, it would signal a remarkable shift from where Democrats and Republicans thought the debate was headed after the tumultuous August recess," reports Carrie Budoff Brown at Politico.

But the proposed move is already gathering opposition from some centrist and conservative Democrats. ABC's Jonathan Karl reported:

This is not a done deal. I am told that Senate Finance Chairman Max Baucus (D-MT) – who worked for months to get Olympia Snowe’s support for the bill and has consistently said a public option cannot pass the Senate – was apoplectic when Reid told him he wanted to include the public option. “Baucus went to DEFCON 1,” said a source familiar with the negotiations, referring to the alert level the military uses for an imminent attack on the homeland.

According to the New York Times, Reid and other congressional Democratic leaders were headed to the White House late Thursday to discuss the idea with President Barack Obama and ask him to help shore up support for it in the Senate.

Sen. Tom Carpenter (D-DE) told TalkingPointsMemo's Brian Beutler that he believes the final public option plan would likely be run by a non-profit organization that is kept at arm's length from the federal government.

"I think at the end of the day there will be a national plan probably put together not by the federal government but by a non-profit board with some seed money from the federal government that states would initially participate in because of lack of affordability," he said. "The question is should there be an opportunity for states to opt out later on and if so, within a year, within two years, within three years?"

Both the House and the Senate are expected to vote on health care reform in the coming weeks. Proponents of including a public option in the reform were recently boosted by polls showing growing support for the idea among Americans, as well as a Congressional Budget Office estimate that said the public option would actually reduce the federal government's deficit, rather than adding to it.