This is in keeping with his pledge to veto legislation that replaces the sequester with spending cuts alone or eliminates it altogether. It also aligns him with Congressional Democrats, who have been telecasting this legislative strategy for a couple weeks.
Meanwhile Republicans have been steeling themselves to let the sequester hit if Democrats won't agree to replace it with spending cuts only. So the Obama-Reid approach has the added political benefit of saddling Republicans with the consequences if the sequester hits. Voters will hear that Republicans prefer the sequester to raising even a small amount of revenue from oil companies and other unpopular interests -- that the only thing Republicans want more than the sequester is a wide range of cuts to services for the poor. Defense contractors will hear that their Republican allies are prepared to abandon them unless and only unless Democrats agree to cut social insurance programs.
That will put a lot of pressure on the GOP to cut a deal. The irony is that if Republicans were to take the Democrats up on their small bore, but politically expedient, revenue proposals -- like eliminating oil and gas company tax preferences, implementing the Buffett Rule, or even doing away with the carried interest loophole -- it would only delay the sequester temporarily. Eventually Democrats would run out of "gimmicky" revenue raisers, and have to fight over the rest of the sequester on less politically advantageous terrain. If they have an upper hand in the political fight right now, its because Republicans have made their own irrationality about taxes a safe bet.