As President Trump heads into the fight of his political life, the man he had hoped would help guide him through it has now turned him down, and he finds himself in the unaccustomed position of having no obvious second option.

Nick Ayers, the main focus of President Trump’s search to replace John F. Kelly as chief of staff in recent weeks, said on Sunday that he was leaving the administration at the end of the year. Mr. Ayers, 36, the chief of staff to Vice President Mike Pence, is returning to Georgia with his wife and three young children, according to people familiar with his plans.

The decision leaves Mr. Trump to contend with fresh uncertainty as he enters the 2020 campaign amid growing danger from the Russia investigation and from Democrats who have vowed tougher oversight, and could even pursue impeachment, after they take over the House next month.

As the president hastily restarted the search process, speculation focused on a group that was led by Representative Mark Meadows, a North Carolina Republican who is the hard-edge chairman of the conservative House Freedom Caucus, but also included the Treasury secretary, Steven Mnuchin; Mr. Trump’s budget director, Mick Mulvaney; and the United States trade representative, Robert Lighthizer.