White House Chief of Staff Denis McDonough met Thursday with about a dozen Senate Republicans in hopes of charting a path toward a potential budget deal, but aides cautioned that the session was mostly informational and unlikely to produce significant progress.

The Capitol Hill meeting was designed as a follow-up to two recent dinners President Obama hosted for Senate Republicans in search of a “caucus of common sense” that could agree on a plan to raise taxes, cut entitlement spending and replace sharp automatic cuts known as the sequester. Obama has argued that such a deal would stabilize the national debt and permit Washington to move on to other issues after two years of battling over taxes and spending.