WASHINGTON — Big worries for the nation’s first high-tech census should have been obvious when tests showed some of the door-to-door head-counters couldn’t figure out their fancy new handheld computers.

Now, officials say, technology problems could add as much as $2 billion to the cost of the 2010 census and jeopardize the accuracy of the nation’s most important survey.

Census officials are considering a return to using paper and pencil to count every man, woman, and child in the nation.

At more than $11 billion, the initial cost of the 2010 census was already the most expensive ever. Officials now are scrambling to hold down costs while trying to ensure the count produces reliable population numbers — figures that will be used to apportion seats in Congress and divvy up more than $300 billion a year in federal and state funding.

“What we’re facing is a statistical Katrina on the part of the administration,” Rep. Carolyn Maloney, a New York Democrat, said “Will they leave this mess for the next administration?” Maloney asked, a member of the House committee that oversees the census.

This was to be the first truly high-tech count in the nation’s history, with census-takers using handheld computers to track and tally the millions of Americans who do not return the census forms mailed out by the government. The Census Bureau plans to hire and train nearly 600,000 temporary workers to help.

But interviews, congressional testimony, and government reports describe an agency that was unprepared to manage a $600 million contract for the handheld computers that will be vital. Census officials are being blamed for a poor job spelling out technical requirements to the contractor, Florida-based Harris Corp.

The computers proved too complex for some temporary workers who tried to use them in a test last year in North Carolina. Also, the computers were not initially programmed to transmit the large amounts of data necessary.