In addition, funding for the bank-rescue plan is unlikely to exceed the $350 billion currently available under the TARP, another source said.
"We are going to have to work with the banks in an effective way to clean up their balance sheets so some trust is restored in the marketplace," President Obama said in a press conference Monday night.
A Treasury Department source said the plan was essentially complete with only minor “tweaks” being applied. The plan was presented to members of Congress this evening, according to sources.
The package will be unveiled Tuesday by Treasury Secretary Timothy Geithner at 11 am EST. CNBC.com will carry the speech live.
CNBC will also interview Geithner after the speech at 12 Noon EST. It will be his first television interview since becoming Treasury Secretary.
Before taking over Treasury, Geithner was president of the New York Federal Reserve Bank and worked on the prior administration's rescue effort but acknowledged it was inadequate and unpopular.
"The spectacle of huge amounts of taxpayer money being provided to the same institutions that helped cause the crisis, with limited transparency and oversight, added to public distrust," Geithner said in remarks prepared for delivery when the new measures are released.
He pledged banks will go through "a carefully designed comprehensive stress test" in future to make sure their balance sheets are clean and they meet requirements for capital.
Congressional sources briefed on the Treasury's plan say it will have four elements.
—Among them will be a plan to use existing funds from the Troubled Asset Relief Program and financing from the Federal Reserve to encourage private investors to purchase assets off the books of the banks.
This plan could come in one of two ways: either the investor could be insured against further losses below a certain level after purchasing assets, or the government could finance the purchase of those assets.