Updated at 3:04 p.m. ET on 7/17
(CNN) - It was a suggestion made quickly to a reporter in a Capitol hallway.
But now that Sen. Lindsey Graham is on the record as suggesting a boycott of the 2014 Winter Olympics in Sochi, Russia, the South Carolina Republican says it could be a consideration if Vladimir Putin allows NSA leaker Edward Snowden to remain in his country and continues supporting Syrian President Bashar al Assad.
"I would consider anything to change Russia's behavior," Graham told CNN Wednesday. "What I want to do is get people focused on what Russia's doing to the world."
Part of that effort should also include a change in venue for September's Group of 20 meetings, slated for Saint Petersburg. Saying he wanted to "change Russian behavior, not boycott the Olympics," Graham told CNN's Jake Tapper later Wednesday that President Barack Obama should reconsider his upcoming trip to Russia.
"In September, the G-20 meets in St. Petersburg. Mr. President, President Obama, should you go to St. Petersburg, Russia, for the G-20 Summit, if they give Snowden asylum and they don't change their policy toward Syria and continue to help Iran, should you go? My advice to you is I wouldn't go to St. Pete. I would ask for a change of venue," Graham said. That interview is set to air at 4 p.m. ET on "The Lead."
Asked about the summit Wednesday, White House Press Secretary Jay Carney said it was still Obama's intention to travel to Russia for the G-20 - and that any talk of an Olympics boycott was premature.
"We are continuing to work with the Russian government and other nations on this matter and we hope to see Mr. Snowden return to the U.S. I'm not going to engage in speculation about that and the Olympics are a long way off," Carney said.
Graham told CNN earlier in the day he was introducing a resolution in the Senate this week calling on Russia to refuse Snowden asylum. The former government contractor remains holed up in the Moscow Airport transit lounge, and Russian authorities have said in the past they would consider an asylum request but that it will take months.
Graham's resolution won't include any mention of the Olympics, but he said Wednesday that as long as people are talking about ways to grab Putin's attention, a boycott could remain on the table.
"It's something I was asked about, but now that we're talking about it, we're going to have to find a more effective way of dealing with the Russians," he said. "They're wreaking havoc. Their allies in Iran are keeping Assad in power. They're giving Snowden asylum. That's a real slap in the face to our country."
Long a vocal critic of Putin's, Graham wondered about the message it would send to other countries if United States athletes head to the Russian mountains next winter.
"Let's say a year from now there are 200,000 people dead in Syria...Snowden's given asylum in Syria. What are we supposed to do, say 'Let's go to Russia for a party?'" he wondered.
The last time the United States boycotted an Olympics, Moscow and Washington were also at odds. Americans, along with athletes from more than 60 other nations, skipped the 1980 Summer Games in Moscow as retaliation for the then-Soviet Union's invasion of Afghanistan a year earlier.
A boycott was proposed in 1936, when Hitler-run Germany hosted the games. When black and Jewish athletes were barred, some Americans suggested the U.S. refuse to participate, though after the ban was lifted Americans did attend.
Graham, raising the history of those Games, didn't go as far as comparing modern Russia to the Third Reich.
"I'm not saying Russia is Nazi Germany, I'm saying it's a rogue regime that's aligned itself with some of the worst actors in the world stage," he said.
Graham's suggestion wasn't met with much enthusiasm from fellow Republican, House Speaker John Boehner, who called an Olympics boycott "dead wrong" on Wednesday.
"Why would we want to punish U.S. athletes who have been training for 3 years over a traitor who can't find place to call home?" he wondered.
The U.S. Olympic Committee, mindful of their members' long training schedules, also came out against Graham's suggestion of a boycott.
"If there are any lessons to be learned from the American boycott of 1980, it is that Olympic boycotts do not work," USCO spokesperson Patrick Sandusky said. "Our boycott of the 1980 Olympic Games did not contribute to a successful resolution of the underlying conflict. It did, however, deprive hundreds of American athletes, all whom had completely dedicated themselves to representing our nation at the Olympic Games, of the opportunity of a lifetime."
But Graham insisted that even talking about the move could raise awareness of Russia's intransigence on world affairs.
"Women I've met who have been gang-raped by Assad's forces in refugee camps, that doesn't make a whole lot of news. Maybe talking about sports will," he said.
CNN's Deirdre Walsh, Lisa Desjardins and Kevin Liptak contributed to this report.