President Obama will elevate the controversy over his recess appointment powers to the highest level, with the National Labor Relations Board announcing Tuesday it will appeal to the Supreme Court a lower-court ruling that held his appointments to the board were illegal. That move will put the thorny case straight before the justices, who will have to decide whether Mr. Obama overstepped his constitutional powers when he did an end-run around Congress last year and named three board members — using his recess-appointment powers at a time when the Senate considered itself still in session. In January a three-judge panel...