WASHINGTON -- The battle over health care has played out publicly, in Congress, in presidential speeches and in heated town hall meetings all over the country. It has also been waged in the back rooms of the White House, new visitor logs suggest.

White House aides released logs of more than 1,600 visits between Inauguration Day and Aug. 31, the second batch released this year. The release of the visitor logs came in response to requests for information from news organizations, interest groups and individuals, and is far from...