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When it comes to national security, President Obama has a surprising amount of support from the right.

Despite a recent outbreak of conservative-led criticism toward Obama's handling of the Afghanistan war, the Democratic president has won plaudits from Republicans for his leadership on military matters.

They roundly reject his economic, environmental, health care and regulatory policies. But until two weeks ago, when Obama demurred at sending more troops to Afghanistan, conservatives largely applauded his conduct of the war -- particularly his early deployment of 17,000 troops and his replacement of Gen. David McKiernan with Gen. Stanley McChrystal.

"He moved much more rapidly to replace a commander he was dissatisfied with, who was not performing well, than Bush did in his tenure, and all of that looked very good and very promising," said Frederick Kagan, resident scholar at the American Enterprise Institute.

Karl Rove, former adviser to President Bush and FOX News contributor, praised Obama for keeping on Defense Secretary Robert Gates from the prior administration.

"The stewardship of the Defense Department by Robert Gates is a nice surprise. Gates is a patriot. The question was, 'Would Obama listen to him?' And Obama has," he said.

Likewise, conservatives are impressed that there has not been a precipitous withdrawal from Iraq.

"That's a remarkable turnaround for somebody who, during the early stages of the campaign, was the left's most vocal advocate of immediate withdrawal," Rove said.

Conservatives also see the continuation of Bush-era counterterrorism policies like rendition and indefinite detention as positive signs.

"I think now that he is commander-in-chief, President Obama realizes that those things are absolutely necessary to his arsenal in prosecuting a war against a very shadowy enemy," said FOX News contributor Monica Crowley.

These conservatives, though, see those positives as offset -- if not undone -- by the president's drive to close down the detention facility at Guantanamo Bay and his acquiescence in Attorney General Eric Holder's decision to investigate CIA officers who interrogated terrorist suspects.

On domestic policy, conservatives have welcomed Obama's support for charter schools, despite being opposed to most of his other domestic agenda items.

"I think for a liberal Democrat, it takes a lot of courage to take on the teachers' union and to be that direct and that clear about that kind of change," former House Speaker Newt Gingrich said.

They note, however, that Obama's education secretary rescinded approval of a voucher program for schools in Washington, D.C.

FOX News' James Rosen contributed to this report.