LINCOLN, Neb. — State investigators here are still trying to figure out who sabotaged Scott Kleeb’s campaign for Congress last November with a barrage of automated telephone calls to voters. The unauthorized calls, officials said, distorted Mr. Kleeb’s views and even used a recording of his voice — sometimes arriving in the middle of the night — with the greeting: “Hi, this is Scott Kleeb!”

Several Nebraska state lawmakers were so outraged by the shenanigans that they are pushing legislation that would impose some of the country’s most restrictive regulations on prerecorded campaign calls, both bogus and legitimate ones. Similar bills are in the works in Florida, Michigan, Missouri, Wisconsin and at least a dozen other states, prompted in large part by telephone calls authorized by campaigns during last year’s elections.

“Get rid of them,” said Stan Jordan, a Republican state representative in Jacksonville, Fla., who has sponsored a bill there. “When they first started, this wasn’t much of a nuisance. But it’s epidemic-level now.”

Nearly two-thirds of registered voters nationwide received the recorded telephone messages, which as political calls are exempt from federal do-not-call rules, leading up to the November elections, according to a survey by the Pew Internet and American Life Project, an independent research group. The calls, often known as robocalls, were the second most popular form of political communication, trailing only direct mail, the group said.