Senate Majority Leader Harry Reid says he will support allowing the government to sell insurance in competition with private industry if the White House and Democratic leaders push a health care bill with no Republican backing.

Many conservatives and some moderates oppose the so-called public option. It's in the House bill, but not the Senate version. The White House is trying to reconcile the two bills before Thursday's bipartisan summit.

Reid's office said Friday he will work with the White House and Democratic lawmakers to try to craft a public option that can overcome obstacles such as a bill-killing GOP filibuster.

Some congressional Democrats say they doubt the White House would include a public option in the proposal it will unveil Monday.

A Democratic source told Fox News there was no chance the public option would be revived in the Senate. 

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“We are losing votes on the public option, not gaining them,” the source said.

The Associated Press contributed to this report.