Governor Orr, Nebraska's first female governor, easily defeated Mort Sullivan, an Omaha businessman.
In acquiescing to the designation, Governor Orr imposed a condition that no site would be chosen without local consent.
In 1987, Governor Orr also received a well-publicized appeal from Pope John Paul II.
With the backing of Bush supporters, Governor Orr was named chairwoman of the platform committee at the 1988 Republican National Convention.
After a rough start, Governor Orr seems to have reason for some confidence.
One of Governor Orr's campaign chairman last fall, he has not not otherwise been a party activist.
"The Governor said state law is not the appropriate format," said Doug Parrott, the director of communications for Governor Orr.
Governor Orr has not said whom he will appoint, and Mr. Quayle said he made no recommendation to the Governor.
"I'm going to look for someone who can win and who can be a good Senator," Governor Orr said.
Governor Orr and other leaders of the committee said they expected the debate to center on the "newer issues" as the panel meets this week.