KABUL—The asking price for a house in Kabul's toniest district nearly doubled a week ago, after it became clear that an Afghan assembly would endorse a new security deal with the U.S. A day later, when President Hamid Karzai insisted on delaying the critical pact, the price plummeted back to its previous level.

"Everyone will flee if the security agreement is not signed. Everyone will stop renting houses," said Shafiqullah Mohammadi, who is handling the property. The 37-year-old real-estate agent said he plans to emigrate as well if the deal—necessary to maintain U.S. troops and U.S. aid beyond 2014—isn't sealed.

Until recently, Afghans and U.S. officials alike assumed that, despite Mr. Karzai's posturing, an agreement would eventually be reached. But now, they are beginning to confront the real possibility that American support may completely vanish in the coming months—potentially precipitating the collapse of a state that has few other sources of sustenance.

Few politicians in Kabul voiced support for the president's stance. Even one of his brothers, Mahmood Karzai, has sounded an alarm.

"Already, this is damaging the economy a great deal—the economy will completely collapse if it's not signed," said Mahmood Karzai, who was instrumental in President Karzai's 2009 re-election campaign. "He has to sign it, he has no choice. If he doesn't, I think it will be very dangerous. People will mobilize against him."