The Senate is scheduled to reconvene next week.
Coburn, R-Muskogee, supports Bacharach and Dowdell, though he essentially abstained from voting when Senate Democrats tried to advance Bacharach's nomination past a Republican filibuster in July.
Coburn said Wednesday that he would ask Senate Majority Leader Harry Reid, D-Nevada, to schedule another vote on Bacharach's nomination. Ultimately, he said, it would be up to Reid and Senate Republican leader Mitch McConnell, of Kentucky, to determine when votes will be held.
If the judges don't make it through the Senate before the next Congress begins in January, the president would have to nominate them again, Coburn said.
In a news conference on Wednesday, Reid expressed frustration that he had to try to break Republican filibusters on 17 different judicial nominations. He said he would seek to reform the process by which the minority can block action in the Senate.