Treasury Secretary Timothy F. Geithner finds himself in a familiar position: eager to resume life outside government and facing contentious negotiations with Congress over raising the federal debt ceiling.

The last time he was in this predicament, in June 2011, President Barack Obama persuaded him to stay. This time, Geithner has indicated to White House officials he wants to carry through with his plan to leave the administration by the end of this month, even if a deal on the debt limit isn’t in place, according to two people familiar with the matter.