The two pollsters wrote that an Obama withdrawal would alter the dynamic of whether he or President George W. Bush is to blame for the nation's economic woes, refocusing the conversation on reconciliation and the type of bipartisanship witnessed during the Clinton administration.

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They also called Hillary ClintonHillary Diane Rodham ClintonBiden slams Trump over golf gif hitting Clinton Overnight Cybersecurity: Equifax hit by earlier hack | What to know about Kaspersky controversy | Officials review EU-US privacy pact Overnight Tech: Equifax hit by earlier undisclosed hack | Facebook takes heat over Russian ads | Alt-right Twitter rival may lose domain MORE more qualified than her husband to occupy the Oval Office, though they acknowledged having no indication that she was entertaining the idea of running. Clinton has said repeatedly that she is out of politics and enjoying her work leading the country's foreign policy.

While unlikely to come to fruition, the push by Caddell and Schoen to see another Democrat at the party's helm could give Republicans fodder to argue that Democrats have lost hope in Obama and can't muster enough excitement to back their own candidate.

This isn't the first time Schoen and Cadell have called for Obama to bow out of a reelection campaign. In November 2010, the two opined that Obama should announce he wouldn't run for reelection, in order to seize the high ground and position himself better to achieve real accomplishments during the final two years of his first term.