In pushing to include a government-run health insurance plan in the healthcare 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. 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.