Stephen Rhymer says the comments came after the G-O-P lawmakers spoke with Republican U-S Representative Steve Largent at a luncheon. Largent met with Fallin prior to the Tuesday luncheon.
Rhymer says the lawmakers consider Largent the party's best chance to retain the governorship.
Largent hasn't revealed his political plans. His chief of staff says an announcement will be made in two or three weeks.
Fallin says she'll announce her plans in a few months and that Largent's decision won't be a factor.