It’s worth pointing out that when it comes to persuading Congressional Democrats to authorize strikes on Syria, the White House faces a fundamental conundrum to which there may be no clear solution.

The trouble is that the two main concerns Democrats have can only be addressed with reassurances from the White House that, in the end, undermine one another.

On the one hand, Congressional Democrats, rightly, want a clearer case to be made that strikes on Syria will deter Assad from further chemical weapons attacks, and that “sending a message” or upholding that “red line” will dissuade others from similar attacks.

On the other hand, Congressional Democrats, also rightly, want clearer assurances that limited strikes on Syria won’t lead to deeper involvement, and want it more clearly spelled out how the U.S. will respond — or not respond, as the case may be — if strikes cause the situation to escalate.

It’s hard to address both of these simultaneously. The trouble is that the U.S. needs to keep its full intentions vague in order to make the case that intervention will serve as deterrent goal to Assad and others — further chemical attacks will be met with more force, or “punishment,” to prove that we mean what we say.

But vagueness on that point makes it harder to address the latter concern convincingly. This is precisely what bedeviled John Kerry when he said that if Assad responds to strikes with more chemical attacks, “he will invite something far worse and I believe something absolutely unsustainable for him.” Okay, so why should anyone believe this will be limited, then?

You can see this problem showing up not just in efforts to persuade Congressional Dems to support strikes, but in the failure to persuade the public to do the same. A new Pew poll finds that public opposition to strikes has only grown, surging to 63 percent. And here’s the rub:

The public thinks that the United States must do something to register its disapproval of the use of chemical weapons in Syria. Six-in-ten agree that the U.S. must act to show that the use of chemical weapons is unacceptable. However, even among those who express this view just 42% favor U.S. airstrikes against Syria while 51% are opposed.

A narrow majority of the public (54%) says the U.S. has a moral obligation to stop the violence against civilians. But an even higher percentage (75%) says that U.S. airstrikes in Syria are likely to make things in the Middle East worse.

The public — like Congressional Dems — is already persuaded inaction is not acceptable. But those who accept this premise don’t necessarily accept that strikes are the answer. And even as majorities say we must act, bigger majorities also say we can’t act without making things worse.

It also may be that there simply is no answer to the question of whether strikes will accomplish more good than harm that will prove persuasive enough. Whether you call it a delicate balancing act, or an unresolvable contradiction, it is built into the situation that the White House has created, and it’s hard to see the way out.