Iraqi army troops chant slogans as they recruit volunteers to join the fight against a major offensive by the jihadist group Islamic State in northern Iraq, outside a recruiting center in the capital Baghdad last month. (ALI AL-SAADI/AFP/Getty Images)

When it comes to the current violence in Iraq, Americans blame Iraq itself more than the United States' decision to go to war there, according to a new poll Friday from the Pew Research Center.

But when it comes to America's culpability, there's something of a split. Slightly more Americans blame the withdrawal of American forces from Iraq than blame the war itself.

The poll shows 39 percent of Americans say the United States' withdrawal has "a lot" to do with the current instability and violence in Iraq -- in which Islamic State militants have taken over a large portion of the country. By comparison, 32 percent say the war has "a lot" to do with it.

(Poll respondents were allowed to blame both or neither, so it's not as if the question was an either-or proposition.)

As you might expect, opinions on the matter are polarized, with Republicans more apt to blame the Obama-led withdrawal than the George W. Bush-led invasion and war.

Democrats are slightly more apt to blame the war, but both they and independents are pretty evenly split.

So does that mean Americans think withdrawal was a bad idea? Not really.

The withdrawal, after all, came much more recently. And it's not too much of a logical leap to think that the physical act of removing troops from a country led to an escalation in violence there. That's a pretty uncontroversial view. Blaming a decade-old war, meanwhile, requires more of a logical progression.

In addition, without the war, there is no withdrawal. So it's not like the two aren't closely intertwined.

But it's also interesting that more people blame withdrawal, because people really, really liked the withdrawal and really, really disliked the war.

That almost definitely remains the case today.  The poll reinforces that Americans have very little appetite for any significant involvement in Iraq, with just 39 percent saying the United States has a responsibility to do "something" about the violence there. (The U.S. has technically done "something," sending 300 military advisers to the country.)

So don't expect these numbers to make people start re-thinking withdrawal. After all, only four in 10 Americans blame the removal of troops "a lot." But there will continue to be grousing -- particularly on the right -- about whether it was done the right way.

And at least for now, more blame the withdrawal than blame the unpopular war the necessitated it.