Turmoil in the Republican Party continued Sunday as the GOP leadership struggled to agree on a candidate for speaker of the House of Representatives. The spot has been vacant since former speaker John Boehner resigned in September, citing Republican fracturing along ideological lines. Members of the House made public statements Sunday that showed continued indecision.

Members of Congress favored Majority Leader Kevin McCarthy to fill the spot, but the GOP was plunged into chaos after McCarthy withdrew his bid on Thursday, shocking many party members. Reps. Jason Chaffetz of Utah and Daniel Webster of Florida have been campaigning for the position, though neither congressman is a clear successor.

Former vice presidential candidate Paul Ryan has also emerged as a possible candidate, with many members from inside the Republican Party encouraging the Wisconsin congressman to run for the position. The influential 40-member House Freedom Caucus said Sunday that it would support Ryan if he ran. Ryan said repeatedly Friday, however, that he would not run. 

Speaker hopeful Chaffetz went on ABC's Sunday news show "This Week," to make his case for the position. "We need a fresh face and that's, in part, why I put my name in for the spot," he said. Chaffetz, who serves as chairman of the Committee on Oversight and Government Reform, has made a name for himself in his six years in government as someone concerned with government accountability and immigration reform.

Chaffetz is relatively new to government, however, and ABC's Martha Raddatz asked the congressman if he would be able to unify the divided party. "If there's somebody better who can unite us then I'll support them, but you're either part of the solution or part of the problem," he responded. "And right or wrong, I've thrown myself in there and said 'Hey, I think I can do this.' "