My recommendation is not to pay too much attention to the initial posturing by either side. That's the same thing I tell people when I mediate disputes in litigation. Initial demands and offers should always be taken with a hefty dose of salt. These positions are often deliberately designed to communicate just how tough a negotiation the other side can expect. Since parties do not expect the other side to jump at an opening offer, they almost always set them too high (or too low) to give the offering party room to negotiate. Sometimes parties want the other side to think they are crazy or unreasonable. That means it usually doesn't help to express outrage at anything said in the opening rounds of a negotiation. There is little reason even to take these opening statements seriously.
It's the second round of offers where negotiations get more interesting. In that round, the Republicans will probably let the Democrats know what they might be willing to do to raise revenues. The Democrats might be willing to let the Republicans know what steps they might be willing to consider to reduce the growth of entitlement programs. The parties could be discussing a total overhaul of the tax code as a means of satisfying both the Republican demand to keep rates low, and the Democratic demand to raise revenue.
Soon, however, it will be time to pay attention. Because what will determine the outcome of these budget negotiations will be the expressed feelings of the American people, and the strength and volume with which the advocates for the Democratic, the Republican, or some in-between positions express their points of view.
If you are afraid the president might give away too much in the negotiations, it's up to you to support the president and Congressional Democrats vociferously. We should have learned from this election that strong support is the best way to strengthen his hand.