Cole, the chairman of the National Republican Campaign Committee, is "abandoning" social conservative candidates by pulling ads for Reps. Marilyn Musgrave, R-Colo., and Michelle Bachmann, R-Minn., FRC Executive Director Tony Perkins said.
Perkins called the decision to pull ad money for Musgrave and Bachmann "a grave error in judgment."
"The left is attacking both of these outstanding women because they are true conservatives," Perkins said. "They vote pro-life and pro-family."
Bachmann has been criticized recently for saying on MSNBC's "Hardball with Chris Matthews" that Democratic presidential nominee Barack Obama and other members of Congress hold "anti-American" views.
Musgrave is considered a champion of socially conservative causes and one of the most outspoken House members on the issue of gay marriage.
Perkins wrote that both candidates are in "winnable districts," and that "pulling funds from their campaigns "sends the wrong message to their supporters and gives their opponents a chance to produce headlines," the newspaper reported.
"This is no time to cut and run from a fight," Perkins said.
Karen Hanretty, a spokeswoman for the committee, denied funds were withdrawn from Bachmann because of her "Hardball" appearance. She said the congresswoman has more than $1 million cash available and is in a district that has been safely Republican.