Sen. Elizabeth Warren, as well as three other Democratic Presidential hopefuls Sen. Kirsten Gillibrand, Gov. Jay Inslee and react to questions during the Daily Kos/Netroots Nation candidate forum, at the Convention Center in Philadelphia, PA, on July 13, 2019.

A new study from the University of Pennsylvania's Wharton School finds that Sen. Elizabeth Warren's proposed wealth tax on the richest Americans will generate at least $1 trillion less than what the campaign claims, potentially undermining the key funding source for her plans to expand government-backed health care, education and other programs.

Warren's tax, if implemented in 2021, would raise $2.3 trillion to $2.7 trillion in additional revenue over 10 years, well below the $3.75 trillion her campaign estimates, according to the study viewed by CNBC.

In other words, the study projects the proposed wealth tax will raise $1 trillion to $1.4 trillion less than the Warren campaign advertises.

"That does mean — to the extent that they're thinking about this money being used to pay for spending priorities and things like that — they will need to figure out how to come up with that difference," Kent Smetters, faculty director for the Penn Wharton Budget Model, said in an interview with CNBC.

In an email to CNBC, the Warren campaign staunchly defended the wealth tax and argued that the Wharton study relies on weak assumptions.

"This analysis does not study Elizabeth's actual plans -- it does not account for the strong anti-evasion measures in her wealth tax and does not even attempt to analyze the specific investments Elizabeth is committed to making with the wealth tax revenue," said Saloni Sharma, the Warren campaign's deputy press secretary.

The Wharton report also said that the proposed tax would result in secondary economic impacts for families not directly subject to the duty.