WASHINGTON — Rep. Kevin McCarthy, R-Calif., is all but assured of becoming the next House majority leader after a lawmaker considered to be a strong conservative challenger declined Thursday to run in the internal GOP race.The affable McCarthy, now the No. 3 Republican in the House, is by no means the top choice among Tea Party lawmakers who believe the current leadership is tied too closely to the party’s establishment wing. But the path for his ascent to the No. 2 spot seemed to clear Thursday as the potential challenger, Rep. Jeb Hensarling of Dallas, said he would not seek the post.The leadership race was triggered by the defeat of Rep. Eric Cantor in his primary in Virginia on Tuesday. Cantor announced Wednesday that he would step down from the majority leader’s position at the end of July.McCarthy will likely still face opposition from another Texan, Rep. Pete Sessions, also of Dallas, but with Hensarling out, a potential regional showdown between the two largest state delegations in the House appears to be easing.Sessions, a committee chairman and McCarthy rival, entered the race early, calling potential supporters on Tuesday night as Cantor was being defeated in his home-state election by a little-known conservative professor, Dave Brat.It’s also possible that another conservative could still enter the race, aides to House Republicans said, but McCarthy has moved quickly to lock down key votes.Hensarling would have posed the most formidable challenge because of his stature among Tea Party lawmakers seeking to elevate one of their own.In a statement Thursday morning, Hensarling said that after “prayerful reflection,” he would not run for the post.