In others, they must be received by the time polls close.
The Postal Service changes worry some voters, who wonder if their ballots will be delivered in time or whether they will have a convenient way to mail them.
Charles Henze, who has voted by mail in California since he first registered, said the cutbacks have him considering whether to get off the permanent absentee voter rolls this year.
Henze, 46, likes to wait until the last minute to cast his vote. Now that he may have to mail his ballot sooner, he is leaning toward voting in person at his polling place in the eastern San Francisco Bay area city of Pleasanton.
"With primaries in particular, by the time you get to voting, the situation can have changed," he said.
It's a somewhat different concern for Nancy Bowers, who lives on a farm outside Fort Rock, Ore., where the post office is under review for closure. She is worried there will not be a drop box close enough to make voting convenient.
"If they make us go somewhere else, some people may have to drive 50 miles," said Bowers, 65. "They'll consider not voting. A lot of people will."
Fort Rock, about 60 miles south of Bend in central Oregon, is nine miles from Bowers' farm. She said if the post office closes, she would have to drive at least 20 miles to drop off a ballot. For the November general election, that could mean driving in snow.
Oregon Secretary of State Kate Brown is considering asking county registrars to establish more ballot drop-boxes at libraries and other public buildings, including shuttered post offices.
In Arizona, where more than 1 million residents voted absentee last year, election officials are advising residents to get their ballots in the mail by the Wednesday before an election. Pima County Recorder F. Ann Rodriguez said the change could have the biggest effect on residents of Indian reservations and others in rural areas who only make weekly trips to town to pick up mail.
"We're going to have to go back and educate voters," she said.
Delays are among the concerns of Ohio Secretary of State Jon Husted, who sent a letter about the processing center closures last week to the postmaster general. He expressed concern that Ohio ballots could pass through out-of-state processing centers on the way to and from voters.
"A ballot leaving the state by its very nature is a problem," Husted said in a follow-up telephone interview.
His spokesman, Matt McClellan, said the longer trip increases the risk of ballots being damaged, lost or delayed. McClellan said those concerns would be magnified in a presidential election year, when the number of voters and mail-in ballots is highest.
California poses a special problem because of its sheer size.
About 40 percent of California voters are registered for permanent absentee ballots, compared with 5 percent in 2000. Nearly 6 million residents voted by mail in 2008, the last presidential election.
The Postal Service has closed four processing centers in the state since 2008 and plans to close 14 more. Some county registrars said the closures already have had an effect.
The secretary of state said mailed ballots took from five to seven days to arrive at county election offices during last year's local elections in areas that lost distribution centers, rather than the normal one to three days.
Gail Pellerin, president of California's county clerks association, said postal cutbacks had delayed ballot delivery and were a major reason some absentee votes went uncounted last year. Pellerin said she has noticed that some voters have begun using private package companies such as FedEx to overnight their ballots.
"There's nothing worse than having to timestamp those in as too late," she said.
Associated Press writers Jonathan J. Cooper in Salem, Ore., Paul Davenport in Phoenix, Nigel Duara in Portland, Ore., Kevin Freking and Hope Yen in Washington, D.C., Julie Carr Smyth in Columbus, Ohio, and Don Thompson in Sacramento contributed to this report.