Cantor's office did not immediately respond to a request to comment on Issa's statement.
Although Smith has not responded directly to his fellow GOP chairman's comments, he promised on Saturday to push ahead with the legislation. His Judiciary Committee still needs to vote on the bill before it can reach the House floor.
Issa, who is a former chairman of the Consumer Electronics Association, is close with the tech community and has been an outspoken critic of SOPA. He had scheduled a hearing for Wednesday to examine the bill's potential negative consequences but canceled it after speaking with Cantor.
SOPA is designed to go after foreign websites that offer illegal copies of music, movies and TV shows with impunity. The bill would empower the Justice Department and copyright holders to demand that search engines delete links to sites “dedicated” to copyright infringement. Ad networks and payment processors would be prohibited from doing business with the sites.
Senate Majority Leader Harry Reid (D-Nev.) plans to bring the Senate version, the Protect IP Act, to a vote on Jan. 24.
Opponents of piracy bill rally on Capitol Hill: Opponents of the anti-piracy legislation will hold a panel discussion on Capitol Hill on Tuesday. Speakers will include Alexis Ohanian, co-founder of reddit; Cato Institute fellow Julian Sanchez; and Jayme White, a legislative assistant to Sen. Ron Wyden (D-Ore.). The event will take place at the Senate Visitor Center at 12:15 p.m.
Wikipedia will shut down on Wednesday to protest the Internet piracy bills, founder Jimmy Wales announced Monday.
T-Mobile defended the Federal Communications Commission in a statement on Friday, criticizing AT&T for the first time since the companies abandoned their plan to merge.
Media mogul Rupert Murdoch took to Twitter over the weekend to criticize President Obama and Google for their stance on the anti-piracy legislation.
--Updated at 6:58 p.m.