WASHINGTON — Under immense pressure from the liberal wing of his caucus, the Senate majority leader, Harry Reid, has told colleagues that he may include a government-run health insurance plan in a health care bill he will soon take to the Senate floor, Democratic senators said Thursday.

Mr. Reid’s latest thinking seemed to reflect a calculated gamble that the 60 members of his caucus could be persuaded to vote for the public plan, if it included some mechanism for states to opt out.

His decision 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.

At a meeting at the White House on Thursday, Mr. Reid informed President Obama 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, which was called on short notice by the White House.

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 does not have the 60 votes ordinarily needed to secure Senate approval for hotly contested legislation.

Democratic champions of the public plan, like Senator Charles E. Schumer of New York, have urged Mr. Reid to take an aggressive posture, by putting the public plan in the bill and forcing opponents to try to strip it out.

“There is a growing sense that we need to lead on this issue and not wait for it to be offered on the Senate floor,” a senior Democratic aide said. “The idea is that it’s better to show some fight.”