The Romney campaign hopes the gaffe could resonate much in the same way that senior adviser Erich Fehrnstrom's "Etch A Sketch" gaffe did last week, quickly going viral and prompting Democrats and rival Republicans alike to question Romney's commitment to a conservative platform.

Already, top surrogate and former GOP presidential candidate Sen. John McCainJohn McCainArmed Services chairman unveils .1B Asia-Pacific security bill Overnight Defense: Trump scolds NATO allies over spending | Flurry of leaks worries allies | Senators rip B Army 'debacle' | Lawmakers demand hearing on Saudi arms deal The case for protecting America's intelligence agency whistleblowers MORE (R-Ariz.) tweeted about the president's gaffe, citing the Etch A Sketch connection.

The White House downplayed the conversation between Obama and Medvedev in a statement Monday.

"Since 2012 is an election year in both countries, with an election and leadership transition in Russia and an election in the United States, it is clearly not a year in which we are going to achieve a breakthrough," deputy national security adviser Ben Rhodes said in a statement.

"Therefore, President Obama and President Medvedev agreed that it was best to instruct our technical experts to do the work of better understanding our respective positions, providing space for continued discussions on missile-defense cooperation going forward."