The House of Representatives passed the Senate version of the bill 219-212 on Sunday. The House also approved a set of changes to the bill, and the changes will soon go before the Senate for a vote.
Kniss said she was excited to witness Obama sign the historic legislation.
"We were all caught off guard by the passing" of the bill when it happened, she said. "Nobody really thought this would go through as quickly as it did."
When she was in Washington just two weeks ago, Democrats only had 200 votes, 16 shy of the House margin needed to pass the legislation.
She said it's been frustrating the watch the bill's momentum fluctuate, but that House Speaker Nancy Pelosi, D-San Francisco, deserves the credit for mustering the additional votes so quickly. She called Pelosi an incredible role model for women in politics and said she and Obama make a strong team.
"I was there shaking his hand and looking him in the eye," she said of the president. "He looks good. He looks refreshed."
Kniss, who chairs the supervisors' Health and Hospitals Committee, said the next task is to examine precisely how the new bill will affect local constituents.
"We spend $1.5 billion on health care annually," she said of the county. "So my job for the next few weeks is to figure out, 'OK, what does it all mean?'"
She said the county has about 450,000 people who are uninsured or underinsured, and officials expect the bill to create or improve coverage for at least two-thirds of them.
"The devil is always in the details, but I think we'll come out well in it," she said.
Kniss said there's also the hefty task of explaining the bill to the public, garnering support and helping residents get as much out of it as they can.
She said the slim margin by which the bill passed makes it especially important for lawmakers to clarify its contents for the public and show them how they can benefit from it.
"A lot of work is ahead," she said. "I intend to be involved with all of it."
During the run-up to Sunday's passage of the bill, as Obama and Congressional leaders continued twisting arms for votes, U.S. Rep. Anna Eshoo, D-Palo Alto, said calls to her office were two-to-one in favor of passing the health care reform package.
"We're right on the verge of, I think, making history," Eshoo said Friday in a conference call with local reporters, calling health care reform "the unfinished business of the American people."
Although some 72 percent of residents of her district, which includes Mountain View, already have health insurance, Eshoo said the health package ultimately will save money and generate positive impacts throughout society.
The bill will provide millions in new funding for 21 community health centers in the district, and reduce by $25 million the cost of uncompensated care by local hospitals and health providers, she said.
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