The president pledged to push through a reform package by the end of the year that would reduce health costs, increase choice and widen coverage.
Congress is currently debating various proposals, and lawmakers are struggling to reach agreement.
Obama said he now saw "broad agreement" on passing a reform, but a few issues still needed working out.
The president has made passing a health care reform bill the top priority of his first year in the White House.
In the past 10 days, he has embarked on an aggressive push to promote his plans, as members of Congress argue over the details of reform.
'Not a game'
In his opening remarks at Wednesday's press conference, the president said Americans were looking to Congress for leadership.
"This debate is not a game," he said. "This isn't about me - I have great health insurance and so does every member of Congress."