On Saturday, Chavez, known for his outspoken anti-American rhetoric, unexpectedly approached President Obama during the Summit of the Americas and presented him with 1970s's leftist manifesto "Open Veins of Latin America: Five Centuries of the Pillage of a Continent."
The book, by Uruguayan writer Eduardo Galeano, has since surged to number two on Amazon.com's booklist, Reuters reports.
Former Speaker of the House, Newt Gingrich lambasted Mr. Obama on NBC's "Today" show this morning. "Everywhere in Latin America enemies of America are going to use the picture of Chavez smiling and being with the president as proof that Chavez is now legitimate, that he is acceptable."
Gingrich said he thinks there is a "shallowness" in how the Obama administration "analyzes" diplomatic situations. "How do you mend relations with someone who hates your country who actively calls for the destruction of your country?" he asked.
On CNN's "State of the Union " yesterday, Sen. John Ensign (R-Nev.) called the exchange "irresponsible."
"When you're talking about the prestige of the United States and the presidency of the United States, you have to be careful who you're seeing joking around with," Ensign said. "And I think it was irresponsible for the president to be seen kind of laughing and joking with Hugo Chavez."
He argued that Chavez "is not somebody the president of the United States should be seen as having, you know, kind of friendly relations with."
On CBS' "The Early Show" this morning Bush White House Press Secretary Dana Perino said the handshake was a break from Bush policy.
"We did not shake hands with Hugo Chavez. We were not friendly with dictators," Perino said.
According to reporters covering the event, Mr. Obama was completely taken by surprise by Chavez's approach and short of making a major statement in ignoring the Venezuelan leader, there was nothing the president could do but accept the gift and greetings.
"It doesn't make sense," Mr. Obama said of the criticism during a press conference in Trinidad and Tobago Sunday.
"The whole notion was that if we showed courtesy and opened up dialogue with governments that had previously been hostile to us, that that somehow would be a sign of weakness."
Earlier during the summit, Chavez said he would work to reinstate a U.S. ambassador to Venezuela (he kicked the formed U.S. envoy out in September).
Watch Dana Perino and Dee Dee Myers debate the handshake on 'The Early Show' below: