The strict Medicaid work requirement at the center of the Republicans’ major policy bill wouldn’t just require millions of poor Americans to prove they are employed to sign up for health insurance. It would also require dozens of states to quickly build expensive and complex software systems to measure and track who is eligible.

This new responsibility for states, whose existing Medicaid computer systems are often outdated, would be accompanied by reduced federal funding through other changes in the bill. The result, according to state officials, software developers and policy experts, could be major failures in state systems for enrolling people in Medicaid.

“That’s how Healthcare.gov happens,” said Julie Brinn Siegel, a former top Biden administration budget official, referring to the Obama administration’s botched launch of the online Affordable Care Act enrollment portal in 2013.

Ms. Siegel and others familiar with Medicaid systems envision problems like websites that don’t load or incorrectly tell applicants they are not eligible. And Medicaid workers may be overwhelmed as they try to run call centers and process applications. The fallout could mean eligible Americans will have their coverage dropped.

Republicans contend that the work requirement achieves twin goals: It ensures that the government directs resources to Americans who are contributing to society, while saving money to help finance an extension of President Trump’s tax cuts.