Recreational marijuana is legal in Colorado and Washington, and medicinal marijuana laws exist in 20 states. New York soon will become No. 21 on that list. But federal law currently prohibits banks and credit card companies from processing pot business transactions.

That may all be about to change.

"Discussion with Justice to bring clarity to these issues for banks are underway," said Steve Hudak, spokesperson for the Treasury Department's Financial Crimes Enforcement Network, or FinCen.

Hudak told CNBC that "banks are obligated to report suspicious activity, but everyone involved is earnestly looking for a solution to this problem."

The problem he referred to is this: Buying weed from an authorized dispensary is legal in many states, but banking laws clearly have not caught up.

(Read more: Colorado's brand-new pot economy)

"Everyone at this point is working together, so it's just a matter of having a lot of different government agencies and bureaucracies ... all on the same page," said Dan Riffle, director of federal policies for Marijuana Policy Project, a lobbying group based in Washington, D.C. "We can find a solution that will make the banking services available to this industry."

He expect that the Treasury and Justice departments will work out the differences in federal and state laws. That will allow banks to lend money to legitimate marijuana businesses and to process their transactions before the end of the first quarter of 2014.

Laws legalizing recreational or medical pot—or both—are passing on ballots throughout the country, and governors are keen to tap into the potential tax receipts from marijuana sales. Colorado, for instance, expects to generate $70 million in tax receipts from sales this year.

"The issue here is federal law," Riffle said. "A lot of these businesses are going to need access to financing in order to get started. And because of federal laws, banks are unwilling to do business with marijuana-related dispensaries, because of fear of money-laundering charges."

As a result, he said, there's great interest in setting up private equity firms that "can provide start-up financing and capital to these businesses."