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Too little, too late — that’s the message some customers plan to send Internet domain registrar GoDaddy today, after the company gave its support to the controversial Stop Online Piracy Act (SOPA), then withdrew it, but only after customers began transferring domains away en masse.

On Thursday December 22, a user on “social news” site Reddit started a thread calling for customers to drop their GoDaddy domain names over the company’s support of SOPA, also known as H.R. 3261, a proposed anti-piracy bill that would allow the government to block sites accused of copyright infringement. Critics worry the bill’s vague wording would lead to the government knocking sites offline at the behest of industry accusers, culminating in Chinese-style Internet censorship.

(MORE: GoDaddy Reverses Position on SOPA, Yanks Support)

Users just before Christmas marked December 29 (today) as the moment customers should abandon GoDaddy to protest the company’s support of SOPA, but that hasn’t stopped several from jumping the gun: An estimated 37,000 customers abandoned the service by December 24, and the latest figures put the latest figure at over 70,000 (GoDaddy is the world’s largest ICANN-accredited registrar, with over 40 million domain names in 2010).

Major tech players have come out in opposition to SOPA, including AOL, Google, eBay, Facebook, Twitter, Wikipedia and Yahoo. Being on or off the support list has become a kind of lightning rod for opprobrium from consumers, media pundits and Internet activists, all of whom agree that piracy’s a problem, but that SOPA ranges too far (and too nebulously).

GoDaddy withdrew its support for SOPA on December 23, writing in a press statement that “Fighting online piracy is of the utmost importance, which is why Go Daddy has been working to help craft revisions to this legislation – but we can clearly do better… It’s very important that all Internet stakeholders work together on this. Getting it right is worth the wait. Go Daddy will support it when and if the Internet community supports it.”

Some see GoDaddy’s positon reversal as a cynical flip-flop, however, marking December 29 as a day to punish the company further.

MORE: GoDaddy Threatened by Boycott for Supporting SOPA

Disclosure: Time Inc. parent company Time Warner supports SOPA legislation.

Matt Peckham is a reporter at TIME. Find him on Twitter at @mattpeckham, Google+ or Facebook. You can also continue the discussion on TIME’s Facebook page and on Twitter at @TIME.