Primary sweep has Romney 1 win from GOP nomination Mitt Romney has swept all the delegates in the Kentucky and Arkansas primaries, putting him within one win of claiming the Republican nomination for president. With all of his primary opponents out of the race, the former Massachusetts governor should get that win next week when voters go to the polls in Texas. Romney won all 75 delegates at stake in Tuesday's primaries, giving him a total of 1,067. That leaves him 77 delegates shy of the 1,144 needed to win the nomination. Texas will have 152 delegates at stake in next Tuesday's primary. Unofficial returns showed Romney winning Arkansas with 68 percent of the vote and Kentucky with 67 percent. Despite leaving the race, Ron Paul, Rick Santorum and Newt Gingrich were on the ballot in both states.