Now the Republicans are in the thick of a debate over oil drilling, and they're again fending off criticism from the likes of Rush Limbaugh over a compromise that would raise taxes on oil companies while paving the way for new drilling off the nation's coasts.
The issue could come to a head this week as energy takes center stage on Capitol Hill.
Mr. Chambliss and Mr. Isakson are standing firm behind their proposal, which started with backing from a "Gang of 10" and now has 20 Senate sponsors. But as the package gains bipartisan support, it also is drawing complaints from Republicans that it undercuts GOP momentum on the year's most high-profile political issue.
The senators have taken heat from congressional colleagues, including from other Georgia Republicans. Rep. Phil Gingrey of Marietta has said the senators are engaged in "procedural pleasantries" while Rep. Tom Price of Roswell contended their approach "doesn't make any sense to me."
Mr. Chambliss and Mr. Isakson dismiss the criticism, arguing that voters want Congress to set aside differences and agree on something that will make a difference -- even if it requires trade-offs.
"Usually if the extremes are raising Cain, it means you're doing something right," said Mr. Chambliss, who spearheaded the compromise along with Sen. Kent Conrad, a North Dakota Democrat. "We think if anything is going to get 60 votes, it's going to be our proposal."
The plan would allow drilling 50 miles off the coasts of Virginia, South Carolina, North Carolina and Georgia, and the Gulf coast of Florida. It would end tax breaks for the oil and gas industry to generate around $30 billion in revenue, with the money used to offset a massive investment in alternative energy.