Meyer, a Democrat, said she has tried to "hit the new areas" in her re-election campaign.
She said some of the workers had absentee ballot paperwork.
"The vast majority of them that I visited with said, 'We work 16 hours a day, and we have no intention of voting" in North Dakota, she said.
Other lawmakers said they doubted the new residents would be rushing to the polls."I don't think they're going to influence (election results) a lot for the local stuff. They're really just doing their work, and sending money home to their families," said state Rep. Bob Skarphol, a Republican from Tioga.