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.

Earlier this week, the White House considered trying to assemble a group of interested Republicans for further talks, according to Democratic congressional aides. But the administration rejected that approach, and is encouraging Republicans to choose their own negotiating party.

Still, several Republicans involved in the process say there is little interest in setting up another “gang” or “supercommittee” to hold private talks with the White House outside the normal committee structure. Instead, senators are talking to the White House about setting a broad framework for moving forward, and then handing the job of drafting a deal off to the Senate Finance Committee, which has jurisdiction over Medicare as well as tax policy.

Among the attendees at Thursday’s meeting was Sen. Orrin Hatch (Utah), the senior Republican on the Finance Committee. Hatch has said he agrees with Finance Committee Chairman Max Baucus (D-Mont.) that the committee is the best place to negotiate a broad budget deal. Baucus is pressing the committee to work on a comprehensive overhaul of the tax code, which could serve as an inducement to persuade Republicans to lift the federal debt limit later this year.

In addition to McDonough, deputy chief of staff Rob Nabors, economic adviser Gene Sperling and legislative director Miguel Rodriguez attended Thursday’s meeting for the White House.