Washington ? They may not like it, but many House liberals look ready to accept a compromise health care bill, putting Democratic leaders well on the way to delivering on President Barack Obama’s call for overhaul.

After claiming for months they couldn’t vote for a bill without the strongest possible government-run insurance option, liberals are putting aside their disappointment over the weaker version in the legislation for a historic chance to remake America’s medical system.

“The current language is far weaker than what I would have preferred, and I think that is also true of the Progressive Caucus,” Rep. Emanuel Cleaver, D-Mo., a member of the Congressional Black Caucus, said Friday. “But because I did not come up here to participate in gridlock and acrimony, I have told leadership that I am willing to compromise.”

Obama privately told House liberals they should chalk up a win.

Leaders from the Progressive, Black, Hispanic and Asian-Pacific American caucuses met at the White House Thursday evening with Obama, who listened to their concerns and praised their efforts.

“He looked at us and he said, ‘You guys ought to be walking around like you won because you brought back the public option,”‘ said Rep. Mike Honda, D-Calif. He was referring to the fact that prospects for any kind of government-run option looked grim after August’s angry town halls.

House floor debate could begin late next week on the sweeping bill that extends coverage to 96 percent of Americans, imposes new requirements on individuals and employers to get insurance and provides subsidies for lower-income people.