Romney and Obama spar during a 2012 presidential debate. (Mike Segar/Reuters)

If a rematch of the 2012 presidential election were held today, Mitt Romney would win the popular vote over President Barack Obama, a new CNN/ORC International poll finds.

Romney, who lost the popular vote by 3.9 percentage points in the 2012 election, would beat Obama 53 percent to 44 percent, the poll conducted July 18-20 and released Sunday found. A similar survey of registered voters conducted by ABC News and the Washington Post in November found the Republican nominee would have beaten Obama 49 percent to 45 percent, had the 2012 election been held in 2013.

But for those thinking the flip in favor of Romney is cause for GOP celebration, consider that the same CNN/ORC survey found Romney would lose by 13 points (55 percent to 42 percent) against Hillary Clinton, a possible 2016 presidential candidate, in that hypothetical 2016 matchup.

Not that it would ever happen: Clinton says she has not decided whether she will seek the 2016 Democratic nomination; Romney has said repeatedly he won't run.

And Romney's win in a theoretical rematch against Obama is also not necessarily evidence of buyer's remorse — it's more likely indicative of President Obama's dismal job-approval rating. According to Gallup, 40 percent of Americans approve of the job Obama is doing, while a majority (52 percent) disapprove.

Obama's current approval rating is almost as low as it was in August 2011, when 38 percent approved of the job Obama was doing, and 55 percent disapproved.