Obama did not say how the cuts would be averted. He has stipulated in the past that he will veto legislation to undo or rollback sequestration unless it is replaced with a balanced plan to reduce deficits in a more targeted way. That caveat suggests sequestration will take effect unless Republicans agree to raise taxes on higher-income earners -- either with an affirmative vote, or by allowing all of the Bush tax cuts to expire at the end of the year.
Republicans have consistently opposed higher revenues in all budget negotiations, and House Speaker John Boehner recently insisted he'd continue to oppose them even if Obama wins re-election. Indeed, the intent of the sequester was to force Congress to come to an accord on medium-term deficit reduction, but those negotiations faltered because of GOP opposition to raising taxes on high-income earners. More recently, though, a number of rank and file Republicans have acknowledged that an Obama victory would amount to a mandate for higher taxes on wealthier Americans.
Earlier this year, Senate Democrats passed legislation that would temporarily extend all of the Bush tax cuts -- except those that only benefit top earners. House Minority Leader Nancy Pelosi and other Democrats have cited that legislation a straightforward way for Congress to avoid or delay the sequester.