Oswaldo Paya Sardinas was scheduled to visit the White House Friday before flying to Miami to discuss his Varela Project with Cuban-Americans over the next few days. Some of them argue that Paya's plans depend on tolerance from the Fidel Castro regime in Cuba, and that is not acceptable.
"A proposal to work within the communist system is not viable," said Jesus Permuy, president of Unidad Cubana, a coalition of 30 exile groups. "If the government is bad, then that government must be changed."
Luis Zuniga, executive director of the Cuban Liberty County said, "Paya is a messenger of false hope."
Joe Garcia, executive director of the powerful Cuban American National Foundation, believes the Varela project has merit.
"Forty years ago, the debate was in the streets of Miami. Now we have to take the debate to the streets of Cuba," he said.
Paya, 50, met privately with Secretary of State Colin Powell this week, and was applauded at a series of functions in Washington. Miami Reps. Ileana Ros-Lehtinen and Lincoln Diaz-Balart, R-Fla., kept their distance.
"I have nothing personal against Paya, just grave concerns about the Varela project," said Ros-Lehtinen.
Paya also has received criticism because he does not support the U.S. economic embargo of Cuba. He has said any change must come from within Cuba and not from outside.
Garcia said the embargo is not the issue.
"We don't have to debate about the (embargo) law; we have to debate about how to bring about change in Cuba," Garcia said.
During his visit, Paya will attend a public mass and ceremony at Our Lady of Charity in Miami and attend a dinner.
The Varela Project is a petition drive signed by more than 11,000 people in Cuba. It seeks a referendum on whether to create greater personal and political freedom in Cuba. The Castro regime has largely ignored the effort.
The Varela project first came to light internationally during former President Jimmy Carter's visit to Cuba last year.
Paya's trip to Miami follows a visit to Strasbourg, France, where he received the European Union's top human rights award. The National Democratic Institute in Washington also has given him its highest honor.
2014: The Year in Music [PHOTOS]