Today's lunch between Paul Ryan and President Barack Obama raises lots of questions, including this one: Did the Wisconsin representative thank Obama for helping him balance the federal budget within 10 years?

It's not likely, but he probably should have. After all, Ryan's budget is expected to achieve balance largely by banking on many of the policies Obama championed -- including Medicare savings from Obamacare and tax revenues raised during last year's fiscal cliff deal.

Ryan won't reveal details until next week, but at a briefing with reporters yesterday, the congressman said it "doesn't take enormous changes" to bring his budget into balance within 10 years instead of the 27-year trajectory he proposed last year.

In explaining his balancing act, Ryan said "Obamacare drops Medicare spending" which will allow his budget to show lower federal outlays on the program over the next decade. The nearly $600 billion in additional tax revenue raised by the American Taxpayer Relief Act will also winnow the deficit projections in the near term.

"We're not going to refight that," Ryan said about accepting tax revenue his party argued against.

None of this is to suggest Ryan is doing anything wrong. On the contrary, he's accepting the lay of the land and using it to further his genuine goal of balancing the budget. Yet the lesson here for Ryan and his party should be that working together and compromising can do more to help the U.S. fiscal situation than just about anything else.

Perhaps it's a lesson Ryan has already learned. After his lunch with Obama, the congressman issued a statement thanking Obama for "hosting a frank discussion about Washington’s budget challenges" and said "everyone needs to be a part of this conversation. We need an open debate about how best to balance the budget and expand opportunity."

(Deborah Solomon is a member of the Bloomberg View editorial board. Follow her on Twitter.)