One moment in Tuesday’s Senate Armed Services Committee hearing with Gen. David Petraeus crystallized the frustration of those who seek a responsible way out of Iraq. Sen. Evan Bayh, D-Ind., who isn’t running for president, asked plaintively and non-confrontationally: “Can’t you offer some rough estimate of when we can start extricating ourselves?”

Petraeus offered little solace. “If you believe withdrawal should be conditions-based,” he said, “it is just not responsible” to set a withdrawal time line. That, he said, would “jeopardize” the security progress of the past year.

In other words, the commitment is open-ended with no goalpost in sight.

I have opposed setting a withdrawal time line. That would not force Iraqi factions to compromise. Rather, it would goad them to gear up for the final, bloody power struggle. Since no faction could win, this power struggle would further fracture Iraq while Iran and a reborn al-Qaida in Iraq, or AQI, rushed to fill the power vacuum.

But the Petraeus formulation offers no promise that maintaining a large troop presence will enable us to exit. He knows that, despite last year’s gains, Iraq’s stability depends on political reconciliation among Iraqi factions. That may or may not happen – there are no Nelson Mandelas in Iraq.

No wonder Indiana’s Republican Sen. Richard Lugar complained to Petraeus: “Simply appealing for more time is insufficient. Does the administration have a workable strategy …?”

Petraeus did have a strategy behind the surge. Additional troops were supposed to provide the security and breathing space for Iraqis to get their political act together. The concept worked – up to a point. U.S. support bolstered and expanded a Sunni tribal rebellion against AQI. The shrinking of the AQI threat – which had viciously targeted Shiites – diminished support for Shiite revenge killing of Sunnis. Sectarian casualties diminished. But Iraqis have so far been unable to fashion the compromises between factions that could solidify gains.

Tens of thousands of Sunni insurgents and tribal forces who turned against AQI remain on the U.S. payroll because the Shiite-led system won’t absorb them on to the government tab. Radical Shiite militias have been battling the Shiite-led government in Basra and Baghdad.

Some so-called benchmark laws, aimed at reconciliation, have been passed but not implemented. Iraqi security forces, five years on, aren’t yet capable of restoring order without strong U.S. backing. That leaves our forces as the barrier to sectarian killing or intrasectarian slaughter.

Meantime, senior U.S. military commanders are telling Congress that the endless troop commitment to Iraq is overstressing the forces.

So the question haunting the hearings – the question Petraeus and U.S. Ambassador to Iraq Ryan Crocker were pressed to answer – was whether staying longer will improve the situation. Crocker rightly noted that many Iraqis are sick of militia violence; most Sunni and Shiite political factions came together last weekend in public support of the government’s effort to crack down in Basra on the forces of the radical cleric Muqtada al-Sadr.

But in the end, neither Petraeus nor Crocker can guarantee that staying will bring the desired results.

They could only point to clues: the fact that as the violence ebbed last year, Sunni and Shiite parties began making some alliances across sectarian lines based on interests. Another sign: Even al-Sadr seems more interested in winning strength through provincial elections than trying to battle for the streets.

The case for staying on would be stronger, if the White House weren’t setting unrealistic goals for the endgame. Sen. John McCain echoed those too-high hopes by claiming “reachable” success would mean “a peaceful, stable, prosperous democratic state …”

A goal that set forth less exalted expectations – a stable Iraq still struggling to define itself would be sufficient – might address fears that our troop presence will never end. Also helpful would be a stronger, more visible U.S. effort to ensure that Iraq’s large oil surpluses started paying for development and basing costs still covered by U.S. taxpayers – something Republicans and Democrats can agree on.

And a crucial, but missing, reassurance would be signs that the White House had a regional strategy to get Iraq’s neighbors, including Iran, to work for a stable Baghdad.

That clarity was beyond what Crocker and Petraeus could promise, and may have to wait for the next inhabitant of the White House. But bipartisan concerns about lack of a clear endgame will haunt efforts to maintain U.S. troops in Iraq indefinitely. That was the message at the hearings this week.