The Obama folks are correct in saying that Speaker John Boehner was willing to do that during the summer 2011 grand bargain negotiations.
But that proposed deal did not include tax rate increases. Now that Obama extracted higher tax rates on earners over $400,000 in the fiscal cliff deal, Boehner and other Republicans insist that's all the revenue increases they'll agree to.
This comes amid stories that Obama's chief political goal is helping his fellow Democrats win a House majority in 2014 and as his Organizing for Action (formerly Obama for America) is still cranking out press releases about the dire effects of the sequester.
It's not unheard of for a politician to make public threats and private blandishments at the opposing party at the same time.
But it is sometimes awkward. Especially if the threats and blandishments are not entirely credible.
Democrats have some chance of winning the 17 seats they need for a House majority. But it's an uphill climb. Even though Obama won 51 percent of the vote in 2012, he did not carry a majority of House districts.
And there is some chance Republicans will capture the six seats they need for a Senate majority. Seven Democratic incumbents are running in states Mitt Romney carried.
And the retirements of incumbent Democrats in West Virginia, Iowa and, as announced Friday, Michigan may put those seats in play.
As for blandishments, Boehner is not the only Republican who has concluded that Obama is not capable of good-faith negotiating.
Republicans argue that revenues are approaching the norm of 19 percent of gross domestic product and that spending needs to come down more from its historic high of 25 percent of GDP.
They're making a little bit of headway on that by accepting the sequester. Obama's flailing seems unlikely to persuade them to change course.