The Republicans are still talking big, but they have to know their backs are against the wall on this issue. The Democrats will propose a stand-alone bill in January which cuts taxes for 98% of Americans and raises taxes for the top 2% -- and it would be political suicide for the Republicans to vote against that bill. As for the rest, allowing the sequestration cuts to discretionary spending to happen (including small cuts to the military budget), I seriously doubt that would be the disaster that the Republicans (and some Democrats) are making it out to be.
One of the reasons the Republicans are trying to paint this as a disaster waiting to happen, other than their desire to keep the tax cuts for the rich, is because they want to get their fingers on the so-called "entitlements" (Social Security and Medicare). They have never liked either program, and they will happily chip away at both until they can get rid of them. They say it is to help the budget deficit, but Social Security has never contributed a single penny to that deficit and Medicare represents only a tiny part of all discretionary spending (far less than the bloated military spending).
Now Speaker Boehner has come up with a new proposal he wants the president to accept. He says he would agree to allow a rise in taxes for those making over a million dollars a year (instead of $250,000 a year), if the president (and Democrats) would agree to cuts in Social Security and Medicare. The cuts he is talking about now involves replacing the yearly adjustments in those programs to meet the rate of inflation with something called a "chained CPI". This would cut the increases to less than the inflation rate. While it would not be an instant disaster for those on Social Security and Medicare, it would mean their buying power would fall a little further behind each year until they could no longer live on the income they get after several years.
This proposal should definitely be a non-starter for President Obama and the Democrats. Not only would it make unacceptable cuts to programs the elderly depend on to exist, but it would raise far less money by raising taxes only for those making over a million dollars a year instead of $250,000 a year. It's a sham proposal, made only to give people the illusion that the Republicans are trying to negotiate in good faith (which they aren't).