That's no easy task given Murray and the Democrats want to spend $1.058 trillion, and Ryan and the Republicans want to spend just $967 billion. And many Republicans will recoil at giving up any of the sequester cuts unless they get a lower corporate tax rate or some other top priority.
But bridging the basic spending level difference should not be impossible, even though negotiations may go beyond the Dec. 13 deadline set by the latest budget agreement. There are not many legislative days between now and then given holiday breaks so that Dec. 13 date seems fairly likely to slip.
(Read more: Washington gets busy on big to do list)
Meanwhile, there is good reason to believe that House Republicans will refrain from driving Speaker John Boehner (R-Ohio) into another shutdown over efforts to defund and delay Obamacare.
The White House successfully showed it would not give in to such demands, in perhaps the most important development to come out of the crisis. And polling for Republicans, even in fairly safe GOP districts, is now so bad that the appetite for bitter confrontation is likely to be somewhat diminished.
(Read more: DC budget menu? Start with pizza: GOP pro)
Senate Minority Leader Mitch McConnell (R-Ky.), who stepped in to broker a deal with Majority Leader Harry Reid (D-Nev.), when the House GOP failed to agree on a plan of its own, made it clear in interviews late this week that the party should under no circumstances re-ignite the Obamacare battle as part of the next budget fight.
The grand bargain itself is not impossible and President Barack Obama certainly wants to make a deal that reduces the likelihood of big fiscal fights dominating his last three years in office.
(Read more: This is what the shutdown really cost you)
But the president did not do himself any favors at the end of the debt limit fight.
First, Obama enraged many House Republicans by speaking Wednesday night before the chamber even voted on the debt limit bill. Then in his speech supposedly moving past the crisis and laying groundwork for legislative collaboration on immigration and other issues, Obama could not seem to help taunting Republicans by saying if they want to make big changes they should "go out there and win an election."
Republicans, of course, won enough elections to control the House, and many of them won by strongly opposing Obamacare.
In private emails to this columnist, senior House GOP aides fumed over Obama's performance, suggesting it would make cutting any large deal even harder and start the budget talks off on a decidedly bitter note.
But while Obama may have increased animosity between the two sides, the likelihood of another shutdown and brush with debt ceiling catastrophe early next year seem relatively slim.
—By Ben White, POLITICO's chief economic correspondent and a CNBC contributor. White also authors the daily tip sheet POLITICO Morning Money [politico.com/morningmoney] Follow him onTwitter