A Pew Research Center study found that of Fox News stories about Mr. Obama from the end of August through the end of October, just 6 percent were positive and 46 percent were negative.

Pew also found that Mr. Obama was covered far more than Mr. Romney. The president was a significant figure in 74 percent of Fox’s campaign stories, compared with 49 percent for Romney. In 2008, Pew found that the channel reported on Mr. Obama and John McCain in roughly equal amounts.

The greater disparity was on MSNBC, which gave Mr. Romney positive coverage just 3 percent of the time, Pew found. It examined 259 segments about Mr. Romney and found that 71 percent were negative. …

Such stridency has put NBC News journalists who cover Republicans in awkward and compromised positions, several people who work for the network said. To distance themselves from their sister channel, they have started taking steps to reassure Republican sources, like pointing out that they are reporting for NBC programs like “Today” and “Nightly News” — not for MSNBC.