"We're disappointed that the foundations haven't stepped forward," he said.
Their concern: That a new museum will eat into the much-craved receipts of other struggling attractions in Center City - a notion he largely dismissed.
Appearing with Rendell at the ceremony was H.F. "Gerry" Lenfest, whose $40 million donation galvanized ambitions that the museum would be built.
Lenfest in recent years has philanthropically dispensed with much of his more than $1 billion cable-industry fortune. Since the late 2000s, he has been a leader in corralling support for a local museum devoted to the American War of Independence, an insurrection fomented in part by governing elites in colonial-era Philadelphia.
In an interview after the ceremony, Lenfest also dismissed concern the new museum might damage attendance at other sites.
"It's not going to cannibalize," he said. "It's going to help."
Enough has been raised to begin construction in the summer and to open by late 2016 at the site of the long-vacant Independence National Historical Park visitor center, said Michael Quinn, museum president and CEO. The private nonprofit needs about $30 million more for an endowment, as well as $18 million to be ready for opening.
The assembled crowd of donors, onlookers, and others was treated to impassioned remarks from Rendell about the importance of the Revolutionary War.
Those who led the Revolution were aristocrats with untested military capabilities. They took on formidable British troops, Rendell said, making America's anticolonial push extraordinary compared with other independence movements.
"We won our freedom against all odds. And that story needs to be told," Rendell said with Lenfest seated nearby.
The former Philadelphia mayor - credited with generating support to build the National Constitution Center in 2000 - then issued what he called a clarion call for more donations.
"The museum must be built, and it must be endowed properly," Rendell said. "The museum still needs people to step up and donate."
The project is set to move forward after nearly a decade of effort that included a failed bid to build it near Valley Forge National Historical Park.
In 2010, after the National Park Service and neighbors near Valley Forge - site of a major turning point of the war - expressed resistance to a privately run museum, the park service accepted a swap of land with the museum backers.
The park service assumed ownership of 78 acres Lenfest assembled near Valley Forge and gave the group $3.1 million and all but a small section of the visitor center complex, much of which went idle in 2001 when a new center opened on Independence Mall.
During Wednesday's ceremony, which included men shooting muskets and igniting historical cannons and fireworks, officials announced the selection of Philadelphia firm Intech construction as general contractor from a field of five bidders.
Intech founder William Schwartz said union crews would likely begin dismantling the brick structure, erected for the Bicentennial. No explosives or wrecking balls would be employed, he said.
"I think we're looking at just weeks away" for demolition, said Schwartz, whose firm also helped build the National Museum of American Jewish History a few blocks away.
Lenfest, an owner of Interstate General Media, which publishes The Inquirer, said his matching grant had yet to reach its goal among third-party donors.
But with $30 million in state grants approved by Gov. Corbett, plus $10 million from the Oneida tribe of Upstate New York and $22 million from donors in and out of the state, he said, the project was a go.
"We have enough funding to tear down this building," Lenfest said.