Graham, who has shown a willingness to work with Obama on issues like climate change and immigration, said the president will have to revamp his agenda early next year.

"I can tell you with certainty that we are going to grow our numbers in the House and the Senate, and the Obama agenda as you know it will be dead on arrival," Graham told a GOP group in South Carolina on Monday, according to a report by the Hilton Head Island Packet.

Republicans look to be within striking distance of winning the 39 seats they need to take back control of the House, and they expect to make serious inroads in the Senate, where they need 10 seats to reclaim the majority — a steep climb by any measure.

Graham's been one of the Republicans the White House has reached out to with some consistency over the last 20 months, though that relationship seems to have grown more frayed as election season has approached. The healthcare fight in particular tested lawmakers' nerves, prompting Sen. John McCainJohn Sidney McCainOvernight Energy: Lake Mead's decline points to scary water future in West | White House leads opposition to raising gas tax | Biden taps ex-New Mexico lawmaker for USDA post Lake Mead's decline points to scary water future in West Five takeaways from the Biden-Putin summit MORE (R-Ariz.) to warn in March that there would be "no cooperation for the rest of the year."

The unfinished items that could roll over to next year — like an energy and climate bill, immigration reform and taxes — are some of the areas where the widest chasms exist between Democrats and Republicans. On two of those issues, Graham has been a key negotiator between the parties.

Congress will look to handle some unfinished business during a lame-duck session of Congress between Election Day and when the new Congress is sworn into office in early January. Graham said he expected the GOP would at least control the House in the next Congress.

"If the election were held tomorrow, we'd take the House back," he said.