WASHINGTON — Demonstrated loyalty. Political savvy. Personal rapport. And, as a bonus, a decent golf game. President Donald Trump had long made clear the qualities he was looking for in his next chief of staff. And when his first pick turned him down, sparking a frantic search, the president turned to the man he’d already tapped for two previous jobs in his administration: Mick Mulvaney, a blunt, fast-talking former South Carolina congressman turned budget chief who had told Trump months ago he wanted the job. It was an obvious choice to many outside the administration that reflects the challenges ahead: Trump will soon be fighting for re-election as he contends with a House controlled by Democrats eager to use their new subpoena power to investigate his administration and business dealings.