This afternoon, White House officials held a conference call with leading House progressives designed to press the case for strikes against Syria, according to Dems on the call. It provides an interesting window on to the challenges they face in persuading liberal Democrats to back action.

The bottom line for liberal Congressional Dems may be pretty much the same as it is for the public, according to polls: Congressional liberals agree Assad is guilty of horrific atrocities against his own people, but are not persuaded that strikes will dissuade further attacks and remain persuaded that they could create more problems than they would solve.

Dem Rep. Barbara Lee of California, a staunch opponent of military action, tells me that the exchange between members of the Congressional Progressive Caucus and White House officials was “frank” and “forthright” and “candid” on both sides, with “very tough questions” coming from progressive Dems.

Rep. Lee, for instance, says she pressed White House officials on this question: “Even the administration agrees there’s no military solution and there can only be a negotiated settlement, so how does the use of force and strikes move us in that direction?” She also pressed for answers on how we can “mitigate” against “collateral damage” and on “the possibility of a regional conflict breaking out.”

“They assured us they’re taking everything into account,” Lee said. “I do have to say the president and this administration have been very careful and very methodical in how they’ve been approaching this.”

Others on the call pressed for answers about whether more international support would be forthcoming.

Lee, however, says she remains unpersuaded. “They’ve been very persuasive about the intelligence and the fact that we must do something,” Lee says. “They were not persuasive for me that the only option right now is a military option.” She added that on the question of whether strikes “will put Assad in check, I’m just not persuaded that’s the case.”

This, ultimately, may be the dilemma the White House faces in a nutshell. Virtually all of the Dems the White House wants to win over agree the case against Assad is strong, and that doing nothing is unacceptable. That argument has been made successfully. But many Dems still are not persuaded that military violence will change the situation for the better and seem to believe the risks of strikes, even limited ones, outweigh the potential upsides, whatever they are supposed to be.

However, Lee did say other progressives on the call seemed to still be in a questioning mode. The White House still could conceivably prevail, given that many Dems who harbor a liberal internationalist streak seemingly remain deeply uncomfortable with inaction in the face of Assad’s horrors.

“They’re working very hard,” Lee said of the White House. “That’s what coming to Congress is all about.”