Republicans are already pushing back against President Obama's just concluded "fiscal cliff" address, in which Obama said a deal is near but not yet at hand and urged further pressure on Congressional Republicans.

A top aide to House Majority Leader Eric Cantor (R-Va.) tweeted that Obama was making a deal harder with the speech, in which he bragged that he'll be president for the next four years and stressed that Republicans have already caved on higher taxes for the wealthy. Both comments drew hearty campaign-style applause from his audience."If Obama's goal was to harm the process and make going over the cliff more likely, he's succeeding," tweeted Doug Heye.

A top aide to Senate Minority Leader Mitch McConnell chimed in that Obama had changed the terms of negotiations in his speech.

"Potus just moved the goalpost again. Significantly. This is new," wrote Josh Holmes, McConnell's chief of staff.

Immediately after Obama spoke, Sen. Bob Corker (R-Tenn.) went to the Senate floor to denounce Obama's suggestion that Congress consider new tax dollars as an acceptable offset to delaying the automatic budget cuts known as the sequester.

"I know the president has fun heckling Congress," he said of the president's speech. "It’s unfortunate that he doesn't spend as much time working on solving problems as he does with campaigns and pep rallies."

Sen. John McCain (R-Ariz.) agreed, saying that Obama's comments were a  "a cheerleading, ridiculing of Republicans exercise" that would "clearly will antagonize members of the House."

Another senior House GOP aide noted that Obama has for days called on Congress to simply pass a bill to spare the middle class a tax hike. "Now turning off the sequester has to be part of this? Talk about moving the goalposts," he said. "He can’t hold the middle class hostage simply when an agreement is ready simply because he wants to get the sequester done now. That can be handled over the next month or so."