CARTAGENA, Colombia — A Secret Service agent preparing for President Obama’s arrival at an international summit meeting and a single mother from Colombia who makes a living as a high-priced escort faced off in a room at the Hotel Caribe a week ago over how much he owed her for the previous night’s intercourse. “I tell him, ‘Baby, my cash money,’ ” the woman said in her first public comments on a dispute that would soon spiral into a full-blown scandal.

The disagreement over her price — he offered $30 for services she thought they had agreed were worth more than 25 times that — set off a tense early morning quarrel in the hallway of the luxury hotel involving the woman, another prostitute, Colombian police officers arguing on the women’s behalf and American federal agents who tried but failed to keep the matter from escalating.

On Wednesday, in a setback to the reputation of those who protect the president, the Secret Service prepared to fire one supervisor tied to the alleged misconduct with prostitutes on the Cartagena trip, the agency said in a statement. Another supervisor has decided to retire, and a third employee will be allowed to resign, the statement said. Eight other employees remain under investigation.

“These guys have the clearest cases,” said a government official briefed on the investigation, referring to the three who are being pushed out.