Venezuela is the fourth-largest exporter oil to the United States, and many at home feel it is in the country's interest to revive relations. The issue of how the United States should deal with Chavez was a large part of the 2008 campaign.
"I don't want to see the power and prestige of the United States president put at risk by rushing into meetings with the likes of Chavez and Castro and Ahjmenanjad," then-presidential candidate Hillary Clinton told CNN in 2007.
In keeping with his doctrine and campaign rhetoric, Obama said that reaching out to critics in Latin America would only benefit the United States.
"We had this debate throughout the campaign, and the whole notion was that if we showed courtesy or opened up dialogue with governments that had previously been hostile to us, that that somehow would be a sign of weakness. The American people didn't buy it. ... And there's a good reason the American people didn't buy it -- because it doesn't make sense," he said Sunday.
The administration said it would like to see the Cuban government take steps on a number of issues, including releasing political prisoners, discontinuing the practice of taking money from remittances and do more to open up freedom of the press. White House Press Secretary Robert Gibbs said Obama was "pleased with the reaction" he received from Cuba, but it depends what measures they take next.
"The fact that you had Raul Castro say he's willing to have his government discuss with ours not just issues of lifting the embargo, but issues of human rights, political prisoners, that's a sign of progress. ... And so we're going to explore and see if we can make some further steps," Obama said.
Only a few years ago, Obama supported lifting the embargo.
"It's failed to provide the source of raising standards of living and squeezes the innocent," and "it's time for us to acknowledge that this policy has failed," he said in 2004.
But his rhetoric was slightly different this weekend.
"Well, 2004, that seems just eons ago. What was I doing in 2004?" he joked. (He was running for Senate). "It is my belief that we're not going to change that policy overnight. And the steps that we took, I think we're constructive in sending a signal that we'd like to see a transformation."
Some Americans feel that it's time the United States relax restrictions on Cuba. A delegation of lawmakers visited the country this month and pressed Obama to rethink the decades-old policy. Others, especially Cubans in Miami, feel that such a move will only give more leverage to the Castro family.
"How do you mend relationships with someone who actively hates your country?" Gingrich said Monday. "Cuba releases zero prisoners, yet we make nice with Cuba. I'm for doing things methodically and calmly ... things that will work, but I'm not for deluding myself about smiles and words."
Some Republicans believe that Cuba needs to take the first step in mending relations.
"Release the prisoners and we'll talk to you," Sen. Lindsey Graham, R-S.C., said on "Fox News Sunday." "Simple as that. Put up or shut up."
Cuba and Venezuela aside, some other moments also drew criticism, such as Obama sitting through a 52-minute airing of grievances by Nicaraguan President Daniel Ortega.