The hypocrisy, critics say, lies in CNN’s decision to woo Hispanic viewers with a prime-time documentary while still giving Mr. Dobbs a nightly forum. Roberto Lovato, a founding member of Presente.org, a Latino advocacy group, said in a statement, “We won’t allow the network to court us as viewers while, at the same time, they allow Dobbs to spread lies and misinformation about us each night.”

Separately, Mr. Dobbs is also the target of a “Drop Dobbs” campaign by the progressive groups NDN, Media Matters for America, and others. That effort started after Mr. Dobbs repeatedly raised questions about President Obama’s birth certificate.

There is no indication that the campaigns are affecting CNN’s revenue, but they are highlighting Mr. Dobbs’s status as an outlier at the channel, which has sought to position itself as a middle ground of sorts in the fractious cable news arena. Mr. Dobbs is known to be exploring an exit from CNN, and he is viewed as a potential hire for the Fox Business Network, an upstart channel owned by the News Corporation.

The Latino campaign’s Web site, BastaDobbs.com, features a video compilation of past comments by the CNN anchor, including his claim in October 2006 that “about a third of the prison population in this country is estimated to be illegal aliens.” He was apparently referring to federal prisoners, and he later acknowledged the claim was made multiple times in error.

As the timing of the prison comment indicates, there is nothing new about Mr. Dobbs’s controversial stance toward immigration, and CNN executives have argued that his hourlong evening program hews more closely to a newscast.