Last week, with polls suggesting Democrats would win a House majority, the prospect of replacing floor leader Rep. John Boehner, R-Ohio, came up, and Barton, chairman of the House Energy and Commerce Committee, said he would take a shot at it, The Hill, a Washington newspaper, reported.
"If a position in the Republican leadership of the House opens, I'm interested," Barton said.
Meanwhile on Election Day, Pence, the chairman of the conservative Republican Study Committee issued a statement with a strong leadership tone as Democrats won a majority.
"Some will argue that we lost our majority because of scandals at home and challenges abroad. I say, we did not just lose our majority, we lost our way," the statement said.
Republican leadership elections are scheduled for Nov. 15-16.
Notable deaths of 2014 [PHOTOS]