"When we heard it was secret, we wanted to see it even more," the Kentucky Republican told CNN's Kate Boldaun in an interview, noting, "As we speak, my staff is still going around Washington looking for the bill."
Paul also tweeted about his search Friday.
"We are continuing our search for the Obamacare Lite bill!" his Twitter post said. "Do you know where the secret location might be? Has anyone seen the bill?"
In the interview on CNN's "At This Hour," Paul said he thinks there is still "a lot of Obamacare lite in their bill," which he described as elements like an individual mandate and a so-called Cadillac tax that would levy steep taxes on health plans considered generous. This, he said, could also be the reason for the secrecy.
When pressed on whether he has talked to House leadership about getting a copy of the bill, Paul declined to comment on specific conversations.
"I think everybody knows I want to see the bill and that I think they've had a PR disaster by putting it under lock and key and trying to keep it out of the view of legislators and the public," Paul said.
Thursday, Paul tried to track down a copy of the draft, but he said he was denied access to a room when aides inside told the senator there wasn't a bill to see. At one point, a GOP staff member allowed House Minority Whip Steny Hoyer, of Maryland, Massachusetts Rep. Joe Kennedy and a dozen or so reporters into the room to inspect it themselves to see that it was, in fact, bill-less.
"I am heading to the secure location where they are keeping the House obamacare bill, Paul tweeted Thursday morning. "I will demand a copy for the American people."
"This should be an open and transparent process," Paul said Thursday following his search. "This is being presented as if it were a national secret, as if this was a plot to invade another country, as if this were national security. That's wrong."
"If they're not embarrassed about the Obamacare lite bill they have, they should show it to us," Paul said Friday. "But they also need to realize they're not going to be able to do this against the wishes of conservatives."
Paul wasn't alone in his health care escapade. Democratic Whip Steny Hoyer went live on Facebook
Thursday in search of the legislation and Rep. Nancy Pelosi also tweeted in support of the search.
"I'm looking for the House GOP's secret ACA repeal bill since they are hiding it from Members and the public," Hoyer posted on Facebook.
"Just helping out @RandPaul. #ReleaseTheHounds #WheresTheBill," Pelosi wrote with an image of two dogs.