As reported in my last column, polls show that Obama's weakest numbers point to his handling of the economy and government spending, and Cornyn already sees evidence that "Obama's personal popularity no longer carries over into the popularity of his policies."
Republican strategists also think that the looming healthcare battle will hand Republicans a major political issue, just as it did against Hillarycare in the mid-1990s that led to their political comeback in the 1994 elections.
The administration's plan could become a minefield for Obama and his party. Taxing employee healthcare premiums for the first time, restricting Medicare coverage, reducing hospital subsidies, and imposing mandates and price controls on the private healthcare industry are just a few of the poisonous issues that could work to the GOP's advantage next year.
Cornyn, a former state supreme-court judge, is one of his party's sharpest strategists who has risen quickly up the leadership ladder. He admits he has been given "a tough job," but makes it clear that he relishes the challenge.
"I didn't come to Washington to be a wallflower, but to show what one person can do to turn things around. I felt this was the place where I could be most productive," he told me.
Cornyn has history on his side. The party in power tends to lose seats in midterm elections, and Obama's presidency may be no exception. Only two presidents have reversed that trend: Franklin D. Roosevelt in 1934 and George W. Bush in 2002.
Senate Minority Leader Mitch McConnell gives Cornyn "an A-plus" for the way he has handled the campaign chairmanship so far -- particularly his success at fundraising. "He raised almost 40 percent more than his committee raised two years ago and eliminated the committee's debt," McConnell told me.
Meantime, it remains to be seen whether candidate recruitment proves to be as successful, though Cornyn's record thus far has been impressive: former Bush budget director Rob Portman in Ohio, Gov. Charlie Crist in Florida and former Rep. Rob Simmons, who is mounting a strong challenge against Sen. Chris Dodd of Connecticut.
People close to Cornyn say he's politically ambitious and has his eyes on the minority leader's post if he succeeds as campaign chairman next year.
Can success in his new job help Cornyn climb further up the leadership ladder one day? I asked McConnell. "It has for some members, and not for others. I don't think it will be a deterrent for him in the future," he said.