On spending, he expects there will be disagreement over where exactly funds should be cut, but said he sees plenty of room for compromise.

"Everybody's going to be looking for those opportunities [to cut spending]. We won't always agree on where they are, but I suspect that we will be working together a lot this year," he said. "The nice thing about fighting over money is this β€” you're not asking either side to compromise on principle. If we say $100 billion and they say $50 billion, you kind of have an idea where the middle ground is."

Kyl sees similar room for bipartisan cooperation on the debate to reform the tax code, as the president has said that comprehensive tax reform is needed to tackle the government's budget deficit. But Kyl envisions a longer timeline for that project, in part due to the fact that Congress just extended for two years lower tax rates enacted under former President George W. Bush.

"The White House and I know Senate Republicans, and I think House Republicans, understand that in the longer run, starting maybe a year or two from now, we are going to have to make some changes to get a more pro-growth tax code," he said. "That will take a long time to put together, we need to start working on it early in the year. Maybe it won't be ready for a year or so."

Kyl argued that the government is not lacking for tax revenue, and any reform effort should not end with taxes going up for Americans. However, he said he would be willing to consider a reform package that would keep revenues neutral, provided it consisted of "good pro-growth policies."

For the past two years, the Obama administration has had a frosty relationship with business. Kyl said it was "highly anti-business" during that time.

However, the president has taken recent steps to start a thaw, including support for the tax cut package enacted in the lame-duck session. Thursday's announcement that former JPMorgan Chase & Co. executive William Daley would be the president's new chief of staff is widely believed to be another indication that the White House is making more business-friendly moves. Daley also served as commerce secretary under President Clinton.

"It sends a good signal, I think he is respected in the business community," said Kyl.

But despite those steps, Kyl contended that one of the president's key achievements thus far, healthcare reform, may be stifling a prompt economic recovery.

"Until this health care legislation β€” the ObamaCare as it’s called β€” is resolved, you're going to continue to see an incredible amount of uncertainty, which will, I think, in and of itself prevent the recovery in as timely a fashion as it might otherwise come," he said.