Mulvaney is part of the Freedom Caucus, a group of roughly 40 conservatives that has taken a hardline stance on some budget issues and has grown increasingly influential. He said he would support Wisconsin Rep. Paul Ryan as speaker, though the 2012 vice presidential candidate has said he's not interested in the position.
"I think the expectations are for Paul to do a little bit better than John did, but also to allow the conservatives along with moderates and centrists in my party to be more actively involved in what the part was," said Mulvaney, whose district is in South Carolina.
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He also called Florida Rep. Daniel Webster a "dark horse" in the leadership election. A day before apparent frontrunner Kevin McCarthy abruptly pulled out of the speaker race last week, the Freedom Caucus backed Webster.
Mulvaney stressed U.S. debt would be paid regardless of who is speaker. He contended that political turmoil would not extend to the financial world because "the markets know" the U.S. will meet its obligations.
A government closure can put some federal employees temporarily out of work or delay their pay. But it has shown to be a mixed bag for stocks in the past.
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