The number-one question when President Barack Obama unveiled his plan to help states expand prekindergarten programs after his State of the Union address: How are you going to pay for this? After all, a similarly structured program, proposed by the Center for American Progress, a think tank closely aligned with the administration, carried a 10-year price tag of nearly $100 billion—a tall order in very tight fiscal times.

The administration would cover the cost for at least part of the prekindergarten expansion by raising federal taxes on cigarettes and other tobacco products, according to this New York Times story. The story doesn’t say by just how much the tax would go up. But, according to this report, released by the Congressional Budget Office last year, hiking the tax from the current level of $1.01 to $1.51 could trim the deficit by $42 billion over 10 years.

The administration, which has proposed to offer grants to states to expand prekindergarten for impoverished 4-year-olds, has already said it will require a state match to participate in the program. But the story isn’t specific about just how much that match would be.

The administration has also proposed incentives for states that want to extend their programs to middle-class families, as well as new money to help states offer full-day kindergarten, bolster Early Head Start programs for younger children, and expand home-visiting services. It’s unclear if all of that would be covered by the proposed tax increase.

And other policy details remain murky, including the overall price tag of the program, what sort of standards programs would have to meet, how the match would work for states that already offer robust universal pre-kindergarten programs and how school districts would be able to participate. (Pre-K experts: I’m sure there are more, what are they?) We will presumably know much more next week, when the administration is scheduled to release its budget for fiscal year 2014.

And will the proposal to increase the tobacco tax to pay for the preschool program make it more politically palatable? It’s sure to anger the tobacco lobby—as well as lawmakers who would rather use the money for deficit reduction—but some states and many parents may be fans of the president’s proposal.

The Obama administration is also planning to propose some spending cuts, according to the NYT story, but it’s unclear whether that would impact the U.S. Department of Education. Many of the programs that the administration wanted to see consolidated into broader funding streams have already been axed.