The backlash against the PRISM surveillance program, which The Washington Post reported gives the U.S. government a direct pipeline to data from major consumer technology companies — is in full force, with several groups calling for a full Congressional investigation of the program.

Companies reported to be a part of the program include Apple, Google and Facebook. Several of the tech firms have denied participating in or even knowing about PRISM.

On Friday, President Obama defended the surveillance of citizens’ digital and telephone communications, saying that the programs were authorized by Congress and overseen by judges.

It’s unclear what such oversight accomplishes, as my colleague Timothy Lee noted Friday, but many aren’t buying what they consider to be the administration’s excuses for questionable privacy infringement.

On Twitter, which was not among the companies named in the report, several people created parody Twitter accounts in reaction to the reports. One kicked off an account with the message, “Well, I guess at this point there’s no reason not to set up a Twitter account.”

Others showed more anger. Responses to a tweet from the White House about its ConnectEd initiative, designed to promote tech and digital learning in schools, quickly became an open forum for users to vent their concerns.

“But then the NSA would have to sort through a lot of macaroni pictures,” wrote one user.

“Right now may not be the best time for you to be pushing for wider Internet access,” said another.

Internet privacy advocates have decried the government’s secret monitoring. The Electronic Frontier Foundation, which has raised alarms for years about what it calls “domestic spying” run by the NSA, is asking for support to petition Congress for a full investigation of the program. A Progressive Change Campaign Committee petition calling for a similar investigation has gotten nearly 20,000 signatures in 36 hours. A petition from the progressive technology company CREDO has gotten more than 40,000 signatures asking Obama to justify the surveillance.

The backlash has been strong, even as many say they had already believed that the government had such a program in place. An Allstate/National Journal poll taken days before the government monitoring was disclosed found that about 85 percent of Americans believe their phone calls, e-mails and Internet use are accessible to the government and other businesses.

The poll, released Friday, showed that at least 48 percent say they “trust” the government to responsibly use collected information. Still, the survey also found that Americans are generally uncomfortable with the idea of their communication information being monitored.

Only 10 percent of the 1,000 people polled said that they were willing to support “expanded government monitoring of cellphone and e-mail activities” to improve national security, as compared with 44 percent who said they would accept more camera surveillance of public places. Sixteen percent of those polled said they would be willing to support increased censorship of Web sites and restricted access to Internet sources.

Forty-two percent of respondents said they didn’t support any of the above.

Related stories:

Wonkblog: Obama says the NSA has had plenty of oversight. Here’s why he’s wrong.

The next big national intelligence debate

Sign up today to receive #thecircuit, a daily roundup of the latest tech policy news from Washington and how it is shaping business, entertainment and science.