The Georgia senator praised the president for reaching out and said he hoped "we can continue the conversation from tonight."
The dinner came on the same day that Obama unveiled a $3.8 trillion budget proposal that has angered some Democrats with proposed cuts to Medicare and Social Security in an attempt to compromise with Republicans.
Another attendee, Nebraska Sen. Deb Fischer, said most of the talk at the nearly three-hour dinner focused on the budget, although Florida Sen. Marco Rubio, a member of a bipartisan group considering fixes for the nation's immigration system, spoke about the overhaul effort.
"Everyone had an equal opportunity to talk," Fischer said in a telephone interview.
Among the topics were the costly entitlement programs and tax reform, according to Fischer. She said the president understands that the issues and their growth need to be addressed, and she cited his budget proposal to change the way the government measures inflation, otherwise known as the chained Consumer Price Index.
Fischer said she appreciated the president's outreach to the GOP and was hopeful "as most of the members of the Senate that we can keep a good, constructive conversation going."
The Nebraskan also said she appreciated the good steak that was served.
A White House official characterized the discussion over a meal that also included salad, sautéed vegetables and coconut sorbet as constructive and wide-ranging, including the pressing issues at the top of the president's agenda.
Isakson put together the GOP list for the dinner in the White House's Old Family Dining Room at Obama's request. Attending were Sens. Lamar Alexander of Tennessee, Arkansas' John Boozman, Maine's Susan Collins, Idaho's Mike Crapo, Wyoming's Michael Enzi, Utah's Orrin Hatch, Kansas' Pat Roberts, South Dakota's John Thune and Mississippi's Roger Wicker.
Hatch spokeswoman Antonia Ferrier said the group and the president had a "a wide-ranging, and open discussion on a whole range of issues from entitlements to tax reform."
Obama had a similar dinner last month with other Republican senators at a hotel near the White House. The White House official, who spoke on a condition of anonymity because the discussions were private, said the president hoped to have more bipartisan conversations in the coming weeks.
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