The nearly 4-minute piece, produced by Fox and aired on the "Fox & Friends" morning wake-up show Wednesday, slammed Obama's record in a style TV critics pounced on as looking like a partisan campaign attack ad.
An Obama campaign spokesman declined to comment on whether the campaign viewed the video as a Romney campaign ad in disguise, The New York Times reported.
The White House and the Democratic National Committee had no immediate comment. Neither did the Romney campaign nor the Republican National Committee.
The piece -- introduced by co-host Gretchen Carlson as "a look back at the president's first term to see if it lived up to [Obama's 2008 campaign theme of] 'hope and change -- juxtaposed Obama "hope and change" sound bites with "then" and "now" graphics comparing the national debt, jobless rate, food prices, gasoline prices, families with no savings and expansion of the federal food stamp program.
Amid increasingly loud, scary music and warning sirens, it showed panhandlers, people on unemployment lines and foreclosure signs as an Obama voice-over said, "We cannot wait for good jobs and living wages."
Unidentified male voices said in voice-over comments, "Instead of concentrating on job creation, President Obama has concentrated on growing government," and, "We are becoming a society that makes poverty more comfortable."
The comments go unchallenged in the Fox News Channel produced segment.
As the foreboding music reaches as crescendo, newscaster voices speak of fears of "long gas lines of the '70s," "prices going through the roof," an unmanageable national debt and other harsh predictions.
The video then concludes with Obama saying: "That's the power of hope. That's the change we seek. That's the change you can stand for."
The hosts then congratulated the associated producer who made the video.
"Hats off to Chris White," co-host Steve Doocy said.
TV critics and others blasted the video as out of bounds and belying the channel's "fair and balanced" claims.
Baltimore Sun TV critic David Zurawik, who has defended Fox News in the past, wrote, "Even I am shocked by how blatantly Fox is throwing off any pretense of being a journalistic entity with videos like this."
Zurawik pointed out that two years ago he challenged the Obama administration when it sought to limit Fox News access to interviews and other news opportunities on grounds the network was not a legitimate news operation.
But now, he wrote, "Any news organization that puts up this kind of video is rotten to the core."
He warned viewers not to "be fooled by ... all the talk about how some shows are news and some are opinion on the channel."
Fox public relations executives have described "Fox & Friends" as an entertainment show.
Conservative blogger Ed Morrissey wrote on the conservative Web site Hot Air, "If anyone wanted to look for evidence that the overall Fox News organization intends to campaign against Obama rather than cover the campaign, this video would be difficult to refute as evidence for that claim."
The video was removed from the network's Web sites Wednesday afternoon, although it remained available on YouTube and other Web sites.
Earlier in the day, Fox Nation, a conservative arm of FoxNews.com, promoted it as a "must-see Fox video."
Fox News issued a statement late Wednesday.
"The package that aired on 'Fox & Friends' was created by an associate producer and was not authorized at the senior executive level of the network," the statement, attributed to Fox News programming Executive Vice President Bill Shine, said. "This has been addressed with the show's producers."
Shine's statement did not refer to any disciplinary action nor did it apologize for airing the video.