Obama has called Sunday's scheduled vote in Crimea "unconstitutional," but at the same time the White House has sought to focus attention on the fact that the Russians have a vested interest in what happens in Ukraine.
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The president has made that argument twice in phone calls with Russian President Vladimir Putin since Russia's military incursion into Crimea, while pressing his concerns about Russia's actions with other world leaders in recent days.
But with the referendum just days away, Obama now finds himself racing against the clock to persuade Putin that it's in his interest not to alienate himself from the West and Ukraine, while at the same time looking for an off-ramp from the crisis that would allow the Russian president to save face on the world stage.
(Read more: Vitali Klitschko: Putin worried over Ukraine)
While protesting that Russia has violated Ukraine's sovereignty, the White House has also sought to stress that Russia has a legitimate interest in how Ukraine integrates with the European Union.
"We absolutely recognize that Russia has interests in Ukraine and that includes in Crimea," Carney said.
Congress has shown an unusual bipartisan streak as lawmakers collectively have expressed their anger at the Russians since Putin deployed troops into Crimea on Feb. 27.
On Tuesday evening, the House approved a symbolic resolution condemning Russia and calling on Obama to consider tough sanctions against Russia for the military incursion in Ukraine's territory.
Obama signed an executive order last week to allow for the implementation of visa bans and financial restrictions against Russian and Ukraine citizens who are responsible or complicit in threatening Ukraine sovereignty.
(Read more: Will Ukraine crisis impact investors?)
The White House has sidestepped suggestions that the battle to head off Sunday's referendum is fruitless. Earlier this week, former Defense secretary Robert Gates, who served in both the Obama and George W. Bush administration, said that Crimea is gone.