Mr. Horne, who is battling allegations of campaign finance and other ethics violations, is known for his hard-line views on immigration. In speeches and a new television ad, he boasts that he “fought voter fraud” by personally defending Arizona’s proof-of-citizenship rules in court.

Just how many voters will be frozen out of local and state elections is unclear. Here in Maricopa County, which accounts for 60 percent of Arizona’s population, officials said that as of last week, 811 voters were on the federal-only list, but only 303 of them were considered “active voters.”

Based on past experience, intensified voter drives in coming weeks will result in a surge of new registrations, including many from people who do not have birth certificates or other documents at hand, said Sam Wercinski, executive director of the Arizona Advocacy Network, a liberal group promoting “electoral justice.”

Even if some of them eventually muster the needed proof, he said, if they do not provide it before the Oct. 6 deadline, “they will be disenfranchised for the November election.”

Beyond that, no one has statewide data on those who consider registering but are rejected or deterred from applying. For some, the requirements can be cumbersome: Women who married and changed their names, for example, must show not only a birth certificate but also a marriage certificate. An older resident who moved here after decades of voting in another state may have trouble obtaining a birth certificate, or strain to pay the fee to obtain it.

In Kansas, while the federal-only rolls are small, about 19,000 applicants have been placed on a “suspense list” because their state forms are incomplete, in some cases because they did not provide the newly required proof of citizenship, said Dolores Furtado, president of the League of Women Voters of Kansas.

Registration drives here have been complicated by the need to offer different forms. Most applicants fill out the state form if they have the required proof, which for many here is an Arizona driver’s license first obtained since 1996, when citizenship status was registered on licenses. Others use the federal form, ending up on the federal-only roll.