The House GOP had offered a "fiscal cliff" avoidance plan, endorsed by the leadership and by the chairmen of the Budget and Ways and Means committees. (The latter committee is chaired by Paul Ryan.) You can read the entire offer (PDF) at the link. It's odd, spending about half its text reminding the president that he needs to back off what he wants, then reminding him how fantastic the GOP's original plan was.
"After a status quo election in which both you and the Republican majority in the House were re-elected..."
As Obama knows, the most prominent House member running this year was would-be Vice President Paul Ryan. He lost. So it's in his interest to pretend that the election was merely "status quo," with no voter rejection of his budget ideas.
"If we were to take your Administration's proposal at face value, then we would counter with the House-passed Budget Resolution."
This leads into a discussion, complete with sophistry ("structural reforms to preserve and protect the nation's entitlement programs"), of that budget. But they're not proposing that. Here's what they're proposing:
"[$800 billion of] new revenue would be generated through pro-growth tax reform that closes special interest loopholes and deductions while lowering rates. On the spending side, the Bowles recommendation would cut more than $900 billion in mandatory spending and another $300 billion in discretionary spending."
Brian Beutler sees this as a close cousin to what Erskine Bowles proposed to the Supercommittee. The "mandatory spending" reference is to entitlements, namely Medicare, namely raising the retirement age -- something Bowles favored because Obamacare could catch people caught up in the 65-67 danger zone.
The best way to read President Obama's leaked offer to the GOP last week was: "You want to cut Medicare, you're going to have to propose it first." The House GOP has done so, and gone not to the Bowles-Simpson proposal, but to the proposal by the Democratic member of the pair. You see why they included all that opening verbiage about the "status quo" election. The Republicans are offering more than they did in 2011, and they're wearing the "painful cuts" hairshirts. But they leave aside the issue of top-end Bush tax rates. They try to move the conversation back to generic "revenue," which might mean something different to them than it meant to Bowles.