According to a recent tracking poll by Public Policy Polling, the Charlotte mayor was favored by 27 percent of likely voters, followed by the state senator at 24 percent.
"With each passing week it becomes more and more clear that this is going to be a race between Pat McCrory and Fred Smith," said Dean Debnam, president of Public Policy Polling.
In the last tracking poll, Smith and McCrory were tied at 29 percent.
The poll also found 54 percent of Republican voters could change their mind between now and the election.
The Democratic polling firm conducted an automated survey of 551 likely Republican primary voters on March 24. The margin of error is plus or minus 4.2 percent.