The officials say they, too, would prefer that American troops stay in Afghanistan. But “at the right price,” said a senior European diplomat familiar with the American position. “The price that Mr. Karzai is asking is too high for Obama.”

The administration has instructed the lead American negotiator, Ambassador James B. Cunningham, to make one more push this month to bring Mr. Karzai around, officials said. It may consider letting the talks go into November, if necessary. But officials are loath to see the talks become an issue in the Afghan presidential campaign.

This week, the administration also considered sending Secretary of State John Kerry, who has a good relationship with Mr. Karzai, to personally intervene in the talks, American and Afghan officials said. But in a reflection of the administration’s deepening pessimism — and its preoccupation with other priorities — officials decided Mr. Kerry’s time was better spent on an Asian trip that Mr. Obama canceled because of the government shutdown, according to another American official, although that could change if there was movement in the talks in Kabul.

So for now, it is up to Mr. Cunningham, who has told his Afghan counterparts that talks would be suspended until after Afghanistan’s presidential election if no progress was made soon, according to Mr. Faizi and other Afghan and American officials.

Assuming the election takes place on time, it would still push talks to the middle of next year, and many Western officials in Kabul say the election could be delayed until the summer. In the estimation of many Western officials in Kabul and Washington, that is perilously close to the drop-dead date of Dec. 31, 2014. Mr. Karzai, who has served two terms, cannot run for a third.

Adm. James G. Stavridis, who retired in May as NATO’s military commander, said the logistics of organizing a post-2014 force could prove daunting if a deal was not struck soon. Each of the allies has separate logistics, training, supply and transportation requirements, and “we are getting close to the red line for people to be able to put those forces together,” Admiral Stavridis said Friday at a forum in Washington sponsored by the Fletcher School of Law and Diplomacy, where he is now dean.

The impasse in the talks has been apparent to negotiators since late summer, according to Afghan and Western officials. But both sides had kept the divisions quiet until this week, when the presidential palace issued a statement saying Mr. Karzai had told a gathering of tribal elders that he would not allow American military raids to continue after next year.