The Utah Foundation survey of GOP delegates found Herbert and Hatch both had just one point over the 60 percent threshold needed to become the party's nominee. Herbert's closest challenger is former state Representative Morgan Philpot and Hatch's is former state Sen. Dan Liljenquist.
But the poll, conducted by Dan Jones & Associates for the nonprofit research group, has a margin of error of plus or minus 4.43 percent, making the outcome of the convention unpredictable.
"That's right in line with what we've been seeing," Hatch campaign manager Dave Hansen said of the senator's internal polling, also done by Jones.
"It's nice to have that support going in, but that's not going to slow us down from being well-prepared for the convention Saturday," Hansen said. "While we would like 60 percent, if that doesn't happen we'll be ready for a primary."
A primary is also likely on the Democratic side, where the poll found Hatch's 2006 opponent XMission founder Pete Ashdown with 39 percent of the delegate vote, while former state Sen. Scott Howell had 31 percent.
In the hotly contested 4th Congressional District race, Saratoga Springs Mayor Mia Love is leading with the support of 38 percent of the GOP delegates surveyed, followed by former state Reps. Carl Wimmer, with 25 percent, and Steven Sandstrom, with 18 percent.
In the 2nd Congressional District race, author Chris Stewart is the leader, backed by 34 percent of the delegates surveyed. The next-highest response from delegates was that they were undecided, followed by former Utah House Speaker Dave Clark, with 21 percent.
Reps. Rob Bishop and Jason Chaffetz have sizeable leads in the 1st and 3rd districts, respectively, according to the survey.
The poll of more than 400 of the nearly 4,000 GOP delegates was taken April 4-11. The congressional district results have a margin of error of plus or minus 9.1 percent.
For additional information, go to utahfoundation.org.