It didn’t start out well: the 47% of Americans who approved last week of the U.S. air strikes in Libya ordered by President Obama is lower than for any other military action since WWII, according to a new Pew poll. 

By comparison, here are the percentages of Americans who approved of U.S. military action in other post-WWII conflicts:

49% - Lebanon (1982)
51% - Kosovo (1999)
53% - Grenada (1983)
54% - Haiti (1994)
65% - Somalia (1993)
66% - Sudan (1998)
71% - Libya (1986)
75% - Korea (1950)
76% - Iraq (1991)
76% - Iraq (2003)
80% - Panama (1989)
83% - Iraq (1993)
90% - Afghanistan (2001)

The Pew poll gave a sense why the public may be uneasy—just 39% believe the U.S. and its allies have a clear goal in Libya, 60% think military action is likely to last for some time, and voters are split 46%-43% on whether the U.S. and its allies should remove Qaddafi from power or only protect civilians.

Then there’s a problem a thoughtful Bush administration colleague, experienced in foreign affairs, raised to me recently. Mr. Obama has transferred command of the operation from the American military to NATO. And while the NATO’s Supreme Commander (SACEUR) is a U.S. admiral, he receives guidance from the North Atlantic Council (NAC), composed of NATO members.

As my former colleague pointed out:

“Anyone on the Council can raise an objection about the conduct of the operation and they have a history of wading into the weeds. This was why the French walked out of the NATO discussions. They were afraid (reasonably) that moving the operation into NATO would result in watered down-rules of engagement and unwieldy decision-making. This process is even slightly more complicated because NATO set up a ‘NAC-Plus’ arrangement for Libya that includes Arab countries.

“To get agreement on the NATO handover, members papered over a lot of issues, and…we may end up seeing some messy debates in the NAC that impact the operation. It's a little surprising that Turkey hasn’t objected already.

“There is…an element of multilateralism run amok here. One of the usual arguments for pursuing an operation through NATO is that it makes it easier for Europeans to participate. But here one of our major European partners objected and [the decision-making structure] may prolong the operation if it ties SACEUR's hands.” 

Indeed, this rickety leadership structure my former associate warns about may have caused NATO to engage in a moral equivalency, admonishing the Libyan rebels not to attack civilians with language similar to the words earlier aimed at Col. Qaddafi and his regime. But the rebels had not made the same barbarous threats as Col. Qaddafi, who, referring to them as “rats and dogs,” said, "We are coming tonight...we will find you in your closets…we will have no mercy and no pity."

It is unlikely that the last week of newspaper headlines and TV news reports trumpeting that Qaddafi’s troops are on the move and the rebels retreating will strengthen American support for Mr. Obama’s decision. Only Qaddafi’s defeat, surrender or death in an allied strike would likely increase public approval of the Libyan operation.

For those of us who supported Mr. Obama’s decision, we would hope the White House would give their communications efforts on Libya a fraction of the attention they have lavished on this week’s announcement that Mr. Obama is now an official candidate for president.

Karl Rove is a former senior adviser and deputy chief of staff to President George W. Bush. He is a Fox News contributor and author of "Courage and Consequence" (Threshold Editions, 2010). To continue reading his column in The Wall Street Journal, on labor, Wisconsin and Ohio, click here.