This so-called charm offensive is the key to any budget deal this spring, even a small one, and will determine the Republicans’ receptiveness to the president’s offer in his budget to cut Social Security benefits and slash billions from Medicare. “This is an offer, not a starting point for negotiations,” stressed one senior administration official, roughly 24 hours before the White House was to release its fiscal year 2014 budget.

If Wednesday’s bipartisan dinner goes well, as the last dinner with Republican senators did, then the path to a budget compromise this spring and early summer becomes clear: through the Senate. The White House is slowly trying to woo enough Senate Republicans to move a budget deal through the chamber and then pressure House Republicans to act—similar to the script used during the fiscal-cliff deal.

Already, there are a few, small reasons for optimism. Republican senators seem pleased that the president is willing to cut roughly $230 billion in government benefits, including Social Security, by changing the cost-of-living calculations for benefits. “‘Chained CPI,’ means-testing, and age adjustment, I think, will save these programs from bankruptcy and avoid us becoming Greece,” said Sen. Lindsey Graham of South Carolina, who attended the previous private dinner with the president.

“In return, I would raise revenue by flattening the tax code, paying down debt, and lowering some rates,” he added.