Hutchison asked members of the Texas Farm Bureau to find five or 10 people each to vote in March who might vote Republican in November general elections but typically not in Texas GOP primaries.
"I know that without you I would not be here, that you are sticking with me in a very tough race," Hutchison said. "I need to ask you to reach out beyond farm bureau members and help bring people in to the polls that don't usually vote in Republican primaries."
Perry's campaign portrayed those remarks as a signal that Hutchison is uncertain of drawing typical Texas primary voters. Perry spokesman Mark Miner said "she finally conceded that after being in Washington for more than 17 years her record is not attractive to Republican primary voters."
Hutchison alluded to an election day in April. After her speech, she told The Associated Press she doesn't believe she or Perry has the backing right now of a majority of Republican voters. That could lead to an April runoff.
"Things could change, but I think all of us should be looking at the possibility, anyway," she said. "Not a probability, but a possibility."
GOP activist Debra Medina is also in the race. Though she's generally viewed as the third-place contender, behind the better-funded and more well-known Perry and Hutchison, if she garners enough support it could force a runoff.
Perry's spokesman disagreed that there will be a runoff. He predicted Perry will win the race outright in March.