In the U.S., Chinese activist Chen Guangcheng's influence could wane

(CBS News) Chinese dissident Chen Guangcheng spent his first full day in America inside a housing complex in downtown Manhattan on Sunday.

CBS News correspondent Tony Guida reports the repercussions of his arrival are being felt far beyond New York.

Chen Guangcheng arrived in New York to cheers and applause.

After seven years of prison and house arrest, a daring escape from his rural village, and more than two weeks of hospital treatment for the foot he broke escaping, Chen was more than ready for the warm welcome.

"For the past seven years, I have never had a day's rest, so I have come here for a bit of recuperation in body and spirit," Chen said through a translator.

Chen, who is blind, was beaten, and his family threatened for his long crusade against forced abortions in his village. Local authorities spied on him night and day.

Andrew Nathan, who teaches Chinese politics at Columbia University, says the Chinese government acknowledged what the U.S. was insisting: Chen's case was about human rights.

"They didn't say this but tacitly by letting him go, they're acknowledging that he was abused in his local city where he fled from and that he was fighting for people's rights," Nathan said.

Chen vowed he will continue the fight here, but he faces many other challenges in his new world.

Learning English tops the list. He plans to study law at NYU. And like any newcomer, he must find a school for his two children and decide whether to stay here permanently.

While he's busy with all that, Chen's influence back home will suffer.

"Dissidents who've come out of China have pretty much lost their impact on China. They've tried to use the internet and publications and the telephone and so on to maintain networks in China, but they're not really in the game in China," Nathan said.

Chen found relaxation on Sunday in the park. He has not applied for political asylum here, preserving his right to go home.

But previous dissidents have been prevented from returning, and one who tried to sneak back into China was arrested and is still in prison.