Automatic federal spending cuts could jeopardize the federal government’s plans to digitize the 2020 Census, costing taxpayers billions of dollars in the process, the outgoing head of the Commerce Department warned this week.

Rebecca Blank, who has served an unusually long one-year stint as acting secretary, said in an interview that the Census Bureau is on course to modernize data collection for its next big count. That includes allowing Americans to respond to census questions not just by mail, but online or via a smartphone. It also includes efforts to help the government track down information on people who do not respond to surveys.

Those initiatives would help the government save on its biggest census expense: hiring hundreds of thousands of workers to knock on doors and find non-responders. But that will not happen if cuts forced by the federal budget sequester prevent the Census Bureau from putting new technology in place in the next several years, Blank said.

“If those budgets don’t come through in ’14, ’15 and ’16, we will pay for that in 2020,” Blank said. “We can save billions if we do this right. But we have to do the investments.”

The sequester cuts, which are scheduled to last for a decade, have not yet delivered the crippling economic effect in the Washington area that many forecasters had feared — although some economists say the effects will worsen in the months and years ahead. But Blank’s warnings underscore the potential that some of the program cuts could carry long-term repercussions for businesses, the economy and taxpayers.

The 2010 Census cost $13 billion, the most expensive in American history, largely because the cost per household of collecting information jumped by nearly 40 percent. Those costs have risen steadily since 1970, as fewer and fewer Americans respond to census requests by mail. Census officials say their planned reforms would allow them to complete the 2020 survey at the same per-household rate as in 2010, escaping an expected increase.

Commerce officials have not said how much funding the bureau lost this year because of sequestration. But a pro-census advocacy group, the Census Project, estimates that budget cuts have trimmed 2020 Census spending by 13 percent this year.

Blank is a labor economist who joined the Commerce Department as the top economic adviser to then-Secretary Gary Locke in 2009. She has twice served as acting secretary since then, most recently taking over last June after John Bryson resigned amid health issues. In March, she announced she would leave the department to become chancellor of the University of Wisconsin at Madison. Her last day is Friday.

In economist fashion, Blank said she has grown to see the Commerce Department — which houses a variety of federal activities, including the census, the patent office and the National Weather Service — as an agency that “is all pulled together by one thing: We provide public goods that the private sector needs to operate effectively.”

The information collected by the census is a critical public good, Blank said, and its cost and quality requires sustained federal spending. The same is true of weather forecasts and patent provision, she said.

Blank said she worries budget reductions are already hurting the quality of other Commerce Department data-collection efforts, including the business information that helps the agency calculate the nation’s gross domestic product.

“Over time, you will notice this,” she said, “when our data isn’t as useful or effective as it once was.”