WASHINGTON  In pushing to include a government-run health insurance plan in the health care bill, the Senate majority leader, Harry Reid, is taking a calculated gamble that the 60 members of his caucus could support the plan if it included a way for states to opt out.

Mr. Reid met with President Obama at the White House Thursday to inform him of his inclination to add the public option to the bill, but did not specifically ask the president to endorse that approach, a Democratic aide said. Mr. Obama asked questions, but did not express a preference at the meeting, a White House official said.

Mr. Reid’s outlook was shaped, in part, by opinion polls showing public support for a government insurance plan, which would compete with private insurers. Speaker Nancy Pelosi said again Thursday that the House would definitely include a public option in its version of the legislation.

Just six weeks ago the public option appeared to be dying, under fierce attack by the insurance industry. A clear majority of Democratic senators favor a government-run plan. But public statements by other senators indicate that the proposal lacks the 60 votes ordinarily needed to secure Senate approval for hotly contested legislation.