President Obama's decision to launch airstrikes in Iraq was a popular one -- especially among his biggest political adversaries, conservative Republicans.

According to a new Washington Post-ABC News poll, 63 percent of conservative Republicans and 61 percent of all Republicans support Obama's decision to launch the airstrikes. By comparison, 54 percent of Democrats and 49 percent of independents also sign off on the use of force.

Americans overall support the action 54 to 39 percent.

But just because Obama's big decision was a popular one doesn't mean he's suddenly won a bunch of new supporters. In fact, quite the contrary. His approval rating on his handling of Iraq remains at just 42 percent -- unchanged from two months ago when the situation in northern Iraq was deteriorating quickly.

And conservative Republicans -- who are also the biggest supporters of Obama's less-popular decision to arm Kurdish forces against the radical Sunni insurgents -- are only slightly more approving of Obama's handling of Iraq than they were before. While 10 percent of them approved of it in June, 16 percent approve today.

Here's how that looks:

Despite a slight uptick among Republicans, Obama's approval has actually ticked down over the last two months among Democrats and independents -- even as pluralities of these two groups also support the airstrikes.

While conservative Republicans are about as supportive of the airstrikes as they were two months ago, Democrats and independents, who were once significantly more skeptical about the idea, have warmed to it.

Still, though, conservatives are the most hawkish when it comes to Iraq.

Obama's decision to arm the Kurdish forces, meanwhile, earns slightly more disapproval (49 percent) than approval (45 percent). That's curious, because arming sympathetic forces overseas is often more popular than direct U.S. involvement -- in large part because it doesn't involve risking American lives.

While a majority of Republicans back this decision, Democrats are split and independents oppose it by a 55 to 39 percent margin.

The lessons of the new poll?

1. Views of Obama's handling of Iraq are not just about his most recent decisions -- significant as they are. Even among Democrats, this is true. While 53 percent of liberal Democrats support the airstrikes and 47 percent support arming the Kurds, overall 78 percent say they approve of his handling of Iraq.

Clearly the withdrawal of forces from Iraq, which was a promise that helped deliver Obama the presidency, remains a factor -- along with partisan politics, of course. Still, this is one of those rare issues on which Obama is more allied with conservative Republicans than his own base, which will make his future decision-making processes more interesting.

2. For all the talk about how the Republican Party has become more non-interventionist, the situation in Iraq seems to suggest it still clearly remains the more hawkish party. Even with a president of the opposite party whom the GOP base despises, GOPers are still strongly supportive of that president taking military action when they see the U.S. investment in Iraq taking a turn for the worse.

Rand Paul, take notice.

Peyton M. Craighill and Scott Clement contributed to this post.