They are not playing the same game. Obama has specifically offered to compromise on cuts to programs that Democrats consider to be a priority. Republicans have offered to compromise on literally nothing.
Let us look at the Obama proposal to cut $4 trillion over 12 years.
First, we don't touch Obamacare, simply agreeing that it saves $1 trillion over that same time span.
Next, we cut $400 billion from defense spending as agreed by Gates.
Next, we cut another $400 billion from defense spending.
Next, we cut another $480 billion from Medicare/Medicaid, on top of the $400 billion looted to (partially) fund Obamacare.
Next, we cancel the Bush tax cuts "for the wealthy" to raise another $840 billion. (This will have no effect on the economy because the Magic Cupboard theory posits that removing money from the private sector has no secondary effect.)
Next, we pinky swear that if after 12 years we haven't reduced the deficit to 2.8% of GDP, Congress will cut spending and raise taxes. (It helps at this point to forget that the people now in power will likely be retired or defeated by then, that a whole new set of Congresscritters will be seeking to buy a whole new set of votes, and that 12 years of even the 2.8% GDP target deficits yields another 1/3 GDP in new debt. It also helps to be bad at math, since you'll be 22% shy of your $4 trillion target.)
Yup, the Messiah is clearly the very definition of integrity. The way he bravely sacrifices Democrat sacred cows is awe inspiring.