Hyde-Smith's victory secures a 53-47 majority for Senate Republicans in the next Congress, which starts in January.
GOP Sen. Cindy Hyde-Smith's remarks that evoked Mississippi's history of racist violence have made her Senate election against Democrat Mike Espy closer than Republicans would like.
A potential runoff favors Hyde-Smith over Espy as she consolidates Republican support, the poll finds.
Mississippi's governor will pick a temporary replacement for Cochran soon, but a special election for his seat will be held in November.
Sen. Bob Corker, R-Tenn, announced Friday that he will vote yes on the GOP tax reform bill.
On Friday, House and Senate Republicans plan to nail down and release final, joint tax legislation.
Senate Republicans scrambled to ensure support for a budget resolution vital to President Donald Trump's drive to overhaul the U.S. tax code.
Trump's claim came after Senate leaders decided not to vote on an Obamacare replacement bill because of opposition from three GOP senators.