Popular Current member and journalist Abdel-Halim Qandil has said the Rebel campaign signals the imminent downfall of President Mohamed Morsi.
The campaign, which officially began on 1 May, hopes to collect 15 million signatures by 30 June to register opposition to President Mohamed Morsi and his policies and to demand snap presidential elections.
"The end of the Muslim Brotherhood regime is near," said Qandil during a Popular Current press conference in Damietta.
Qandil compared the campaign with the pro-democracy Kefaya movement that played a crucial role in paving the way for the January 25 Revolution.
The Rebel campaign will announce the number of signatures it has collected during a press conference on Wednesday.
Last week, campaigners claimed they had collected some three million signatures in support of their demands.
On Saturday, when President Morsi was asked about the petition during a visit to Addis Ababa, he urged campaigners "not to forget the key principles of democracy."
"Some people say I barely got 52 percent of the vote in [last year's] presidential election [runoff against Mubarak-era PM Ahmed Shafiq]," Morsi said. "But legally and constitutionally, I am the legitimate president."