Such a turnout would easily eclipse the current record set in 1965, when 1.2 million people attended Lyndon B. Johnson's inauguration.
"I think you could have an inauguration that could be in the 3 to 5 million viewership ... either on the Mall or on the parade route," Fenty said.
National Park Service organizers said they're expecting a large crowd but stopped short of echoing Fenty's projection.
"That's a bigger number than we had seen," said Park Service spokesman David Barna.
Still, he said the National Mall could handle such a crowd on the two-mile span between the Capitol and Lincoln Memorial, as well as the parade route on Pennsylvania Avenue.
"We're blessed to have this large, public, open space that will accommodate millions of people," Barna said.
He cautioned, though, that it's difficult to project how many people will attend because of weather factors and the daunting prospect of overwhelming crowds.
"Remember what those big numbers do is scare a lot of people away," he said. "It can have a reverse impact."
Fenty said the crowd estimate is based in part on briefings city officials have received from officials involved in the transition, who want to open up as much space as possible along the National Mall and parade route for people to watch the ceremonies. He also pointed to the size of the crowds that Obama attracted at campaign rallies across the country and his election night acceptance speech in Chicago.
On Monday, California Sen. Dianne Feinstein, who is overseeing Obama's swearing-in ceremony, said on the Senate floor that more than 1.5 million people could descend on the nation's capital.
D.C. Police Chief Cathy Lanier said the department is tailoring its security plans for the "maximum" number of attendees, but when pressed would not give any estimate.
Lanier said the city is ready for the crowds given its experience with large events in the past, such as the Million Man March and Fourth of July celebrations. Her entire force will be on duty, along with 4,000 officers from 93 agencies around the country. There also will be hundreds of firefighters and paramedics on duty.
Many plans are contingent on Obama's Presidential Inaugural Committee, which organizes the parade and is still being formed.
The federal government has provided local authorities $15 million for the event, but Fenty said the city's expenses likely will top that amount. He said D.C. officials will ask federal agencies to cover any extra costs.
In addition, city officials are working to legally accommodate the hundreds or thousands of people who want to rent out their homes to visitors. In D.C., those wanting to offer a short-term rental must obtain a basic business license. However, officials are exploring a way to suspend that requirement. Fenty said he expects to announce the plan later this week.
Some Congressional offices claim upwards of 50,000 requests for tickets, but with only a couple hundred allotted to each member of Congress more and more offices are forced to turn away constituents, reports CBS News correspondent Thalia Assuras.
Also, people claiming they have a ticket for sale are not telling the truth, Assuras reports. If legislation introduced Monday gets passed, scalping a ticket later will be illegal.