Obama has a major TV booking most nights this week.

On Monday, he did Keith Olbermann‘s popular MSNBC program, “Countdown.” On Wednesday, he’ll chat with David Letterman. For the second straight week, Obama is also a recurring face on Bill O’Reilly’s program. “The Factor” host keeps parceling out clips of their Republican National Convention interview.

Some Democrats criticized the Fox gambit, since it boosts O’Reilly and may do nothing for Obama, given that the audience is primarily made up of Republican senior citizens. As “O Force One” flew over Michigan on Monday, I raised that idea with Robert Gibbs, Obama’s communications strategist. He emphasized that, regardless of the media outlet, the goal is simply to get Obama’s message out during this critical phase of the campaign.

Jen Psaki, a traveling spokesperson for the senator, added that the media outreach complimented Obama’s political orientation. “This campaign has never been about speaking to just one wing of the party. We have visited parts of the country where Democrats have never been, and we are competing in parts of the country where Democrats have never competed,” she said. “Speaking to an audience that isn’t necessarily our base is par for the course — and part of the reason why Republicans and independents are taking a close look at Barack Obama,” Psaki added.

This outreach makes sense. Maybe Obama can pick off a few stray Republicans.

At a minimum, he might get more street cred with independents beyond O’Reilly’s base, if they think he proved his mettle under pressure. The hidden cost, however, is empowering O’Reilly to frame the debate.

I was reminded of that problem today during Obama’s press conference. The first question pressed Obama on his favorable remarks about the surge, from one of his feisty exchanges with O’Reilly. The real challenge, apparently, is winning over O’Reilly’s viewers without sounding like their hero.

Fox News is promoting Obama's Thursday appearance.

As Sen. John McCain accepts the GOP presidential nomination on Thursday night, his opponent will enter the “No Spin Zone.”

Yes, Sen. Barack Obama is headed for Fox News, in a bid for Republican votes, by appearing for the first time ever on Bill O’Reilly’s prime-time show. While McCain aims his acceptance speech at voters beyond his base, Obama will be talking to the bright red Republicans who watch O’Reilly’s highly rated show. In the last presidential election, a whopping 88 percent of Fox viewers voted Republican, while only 7 percent voted Democratic.

Obama’s appearance also caps an unusually long and rocky exchange with O’Reilly.

A senior aide to Obama said the controversial anchor “shoved” him during a February altercation in New Hampshire, when O’Reilly tried to confront the Illinois senator to demand he appear on the Fox program. “I’ve worked two [presidential] campaigns, and I’ve never had a member of the press lay hands on a staff member before,” said the aide, Marvin Nicholson, who travels with Obama. Then, at a secret June meeting with Rupert Murdoch, the owner of Fox, and Roger Ailes, who runs it, Obama aired his concerns about the network’s biased coverage and agreed to appear on O’Reilly’s show, according to new reports from Vanity Fair and The Washington Post.

Beyond O’Reilly’s show, Fox News has been under siege this election season by several liberal groups supporting Obama. The channel was shut out of Democratic primary debates, after Democratic activists and bloggers scuttled its attempt to host debates with the Congressional Black Caucus. More recently, Fox was rocked by allegations of anti-Obama bias and racial prejudice in campaigns by Color of Change, a netroots group focused on black issues and civil rights — that was the battle featuring the rapper Nas on the Colbert Report — and a viral video campaign by Brave New Films.

Obama’s exclusive appearance, however, shows that he’s willing to tap the Fox News for potential conservative voters — even as his supporters try to marginalize its political role.