Higher tax rate will hit relatively few in Oklahoma, but payroll tax is rising for 1.9 million workers

Read: Opinion: Deal is better than the alternative, but only a little

Delegation's votes

Cole, among the six members of Oklahoma's congressional delegation who voted for the deal on Tuesday, said “there were enough good things in the bill to override the things I don't like.”

“Contrary to what's widely reported, there were no tax increases in the bill,” Cole said. “The tax cuts of the Bush era were all set to run out. What we did in the bill was save as many of them as we possibly could for as many people as we could. … That's 85 percent of the money for 98 percent of the people. I think that was the appropriate thing to do.”

Sen. Jim Inhofe, R-Tulsa, said the deal “should be seen as a victory for conservatives as it achieves for the first time in decades a bipartisan agreement for permanent tax cuts for a majority of Americans. These tax cuts will help to restore certainty and encourage economic growth.”

Read: Small business mixed on resolution

Lankford was the only Oklahoma member to vote against the deal. In an interview Wednesday, he acknowledged that there were several positive aspects about the bill but said that he couldn't support it because it didn't provide enough deficit reduction.

“The tax increases that were just put in place will increase taxes by about $60 billion a year,” Lankford said. “That still leaves almost a trillion dollars in overspending every single year. So it's obvious this is not a tax fix.”

Cole and other lawmakers said fights over spending will come in the next few months.

“Now it's time for the president to work with Congress to address our $16 trillion dollar debt and find responsible, commonsense ways to cut spending and grow our economy,” said Rep. Frank Lucas, R-Cheyenne.