As Web firms recently pressed Congress to free them from liability for pirated content on their sites, they turned to a natural lobbying technique: starting a viral campaign.

First came the catchy slogan: “Don’t Break the Internet.” Then came pleas for support on message boards, Twitter and online forums. The result: a million people e-mailing Congress and 87,000 telephone calls, according to figures posted on the American Censorship Day Web site.

The campaign illustrated the quick ability of Silicon Valley to generate a massive grass-roots movement to serve its interests. In this case, some of the biggest companies in technology, including Google, Facebook, Microsoft and Intel, as well as thousands of other online firms, want to soften a bill in Congress that could empower law enforcement to shut down their sites if they host pirated content.

Supporters of the measure, the Stop Online Piracy Act, which include Hollywood, the music industry and the U.S. Chamber of Commerce, also tried to use the Internet to their advantage. They tweeted and took to social-media channels, arguing that the legislation would curb the illegal trade of copyrighted movies, software and music. But their efforts hardly made a ripple in the virtual world.

Meanwhile, firms such as Tumblr, Reddit and Mozilla simply posted their concerns on their sites and were able to rally tens of thousands of ordinary users — if not many more — to their side. Along with consumer advocates, these companies are taking part in American Censorship Day, a splashy campaign encouraging consumers to call Congress and express their opposition to the bill.

The viral movement has not been well received by Rep. Lamar Smith (R-Tex.), one of the primary backers of the measure. Smith said he’s open to discussing legitimate concerns in the bill, but he objects to the way critics have framed the issue.

“Claims that this bill will ‘break’ the Internet are unfounded. When one-quarter of Internet traffic is infringing, something is already in need of repair,” he said, adding that “over-the-top rhetoric intended to excite opposition” is clouding the underlying problem of online piracy.

The bill, which has 25 co-sponsors from both parties, is expected to go to markup around Dec. 15 but nothing has been firmly scheduled, according to a Judiciary Committee staffer. A similar Senate bill is expected to go to vote later in the year or early 2012, a Senate staffer said.

Opposition to the bill is growing from the technology world. On Tuesday, the Business Software Alliance, which represents Microsoft, Intel, Adobe and Apple, pulled its support of the legislation, saying that it “needs work” and that some “valid and important questions” have been raised.

That group joined the criticisms previously expressed by Yahoo, which quit the Chamber of Commerce over the matter, and Google, which has threatened to do the same, according to people familiar with the matter, who spoke on the condition of anonymity to protect their business relationships.

Legislative pushes for the bill in both chambers highlight a consensus among lawmakers and some businesses that online piracy and counterfeiting has become a rampant problem that has drained the pockets of media firms, authors, software and filmmakers who are seeing their goods exchanged for free on the Internet.

Yet while they agree with the spirit of the bill, many technology firms are opposed to the measure as it stands. Last week, tech companies including Facebook signed onto a letter from NetCoalition — a group of companies that counts Google and Yahoo as members— urging the House Judiciary Committee to reconsider the bill. These companies say the bill grants the government too much power to shut down sites that host illegal or pirated content.

Markham Erickson, executive director of NetCoalition, said that while his group did not coordinate with those behind the online push against the bill, it was clear that SOPA has touched a nerve with Web companies.

“We haven’t seen a bill as problematic as this for a while,” he said. “This is an unprecedented bill in its scope and how far-reaching and disruptive it would be to Web platforms,” he said.

But the bill’s proponents — which include the Motion Picture Association of America — say that concerns that the bill would damage Internet culture, promote government censorship or encroach on the First Amendment are overblown. Michael O’Leary, the MPAA’s senior executive vice president for global policy and external affairs, said rhetoric comparing provisions in SOPA to Web censorship are “laughable.”

“This bill has due process,” he said. “It covers activities that are, under federal law, illegal, and requires that any order issued is public and transparent.”