WASHINGTON — Treasury Secretary Timothy F. Geithner plans to leave the administration at the end of January, even if President Obama and congressional Republicans have not reached an agreement to raise the debt ceiling, two people familiar with the matter said.

After giving in to Obama’s previous entreaties to stay as long as needed, Geithner has indicated to White House officials and Wall Street executives that he is unlikely to change his departure plans this time, increasing pressure on the president to name a successor, said the people.