It was one of those ohmyGod moments.

Gen. David Petraeus was testifying Tuesday before the Senate Armed Services Committee. Sen. John McCain was pressing him for his opinion on the feasibility of President Obama’s July 2011 deadline to begin troop withdrawals from Afghanistan. Suddenly, the general slumped onto the table.

Fortunately, it was only a case of dehydration. After leaving the hearing room and drinking some fluids, Petraeus returned and quipped, “It wasn’t Senator McCain’s questions.”

But the general’s brief fainting spell, besides reminding us how irreplaceable he is, did focus attention on the critical question about deadlines that McCain had posed.

The Arizona Republican argued that an “arbitrary” deadline undermines confidence in the region that the United States has the will to stay on long enough to secure its objectives. He said Obama’s commitment to a date certain for starting a withdrawal had convinced key actors in Afghanistan that America was “more interested in leaving than in succeeding.”

I don’t usually agree with John McCain, but this time he is right.

I understand why Obama set the deadline, in a speech at West Point on Dec. 1. At a time of economic recession, he wanted to avoid an open-ended commitment a la Vietnam. He also wanted to convey to President Hamid Karzai that, despite a temporary “surge” of 30,000 U.S. troops, Afghans urgently needed to assume more of the security burden.

However, setting such a deadline in public has the perverse effect of undermining the prospects of meeting it. If, as McCain argues, the main actors think we are short-timers, they will hedge their bets and make different choices.

For example, operations to secure the southern province of Kandahar, the Taliban heartland, are going more slowly than expected because of difficulty winning support from local tribal elders. They are less likely to help Americans push back against Taliban fighters if they think U.S. troops will be gone soon.

Another example: Reports are rife that Karzai is angling for a deal with top Taliban, which would make sense if he believes our commitment is fleeting. Of course, he stands scant chance of achieving such a deal; if the top Taliban leaders think U.S. troops are leaving, they don’t need to compromise with him — or us.

As for Pakistani military officials, if they think we’re short-timers, they won’t break their ties with Afghan Taliban leaders whom they will then expect to return to power.

Of course, Obama didn’t say U.S. troops would stream home rapidly in July 2011; in his West Point speech, he said, “After 18 months, our troops will begin to come home.” (The emphasis is mine.)

Secretary of Defense Robert Gates quickly insisted that any withdrawal would depend on conditions on the ground, and Petraeus gave similar assurances to Afghan and Pakistani officials. But that’s not the way the publics of those countries read Obama’s message: They think the Americans will be departing soon. So, it seems, do many of their leaders.

Which brings me back to McCain’s question at the hearings. When pressed to say whether he supported the 2011 deadline, Petraeus stressed that the date would be the “beginning of a process” and that withdrawal would be “conditions-based.”

When asked a similar question by committee chairman Carl Levin, D-Mich., Petraeus replied: “There was a nuance to what the president said that was very important, that did not imply … a search for the light to turn off, or anything like that.”

But McCain kept pushing, asking the general for his thoughts on the book “The Promise: President Obama, Year One,” by Jonathan Alter, whose sources tell him Obama boxed Petraeus into a firm commitment to let the Afghans take over by mid-2011. The book quotes Vice President Biden as saying: “In July of 2011, you’re going to see a whole lot of people moving out. Bet on it.”

Petraeus replied that he supports what the president said at West Point. He added, “July 2011 is not the date we race for the exits, but is the date we begin a responsible drawdown.”

So who’s reading Obama correctly? Key actors in the region think Biden’s take reflects true U.S. intentions. Gates and Petraeus (and Secretary of State Hillary Clinton) have a different interpretation. If Obama isn’t heading for the exits — and if he wants to halt the downhill slide in the region — he should make his own position clear soon.

— Trudy Rubin is a columnist for the Philadelphia Inquirer. trubin@phillynews.com