As Congress haggles over the details of reform, the president is trying to assert his authority on the issue, Schieffer told CBS Evening News Anchor Katie Couric after the event.
"What the president's really trying to do here... is take control of something that he had kind of farmed out to Congress," he said. "He told Congress to come up with a health care reform plan that met his goals for reform, and so far they haven't done it."
In order to push the process along, Mr. Obama "tried to argue that we have no choice but to do this," Schieffer said.
The president has made numerous televised pitches for health care reform so far this month, and that is likely to continue, according to Schieffer.
"The president is a good salesman," he said. "You're going to keep seeing him here as he tries to get control of this once again."
CBS News Capitol Hill Correspondent Nancy Cordes told Couric members of Congress would like to see the president step up his leadership on the issue.
You can watch the video of Couric, Schieffer and Cordes above.
More Coverage of Obama's Press Conference: