"I, quite frankly looking at it this morning, feel very uncomfortable about where they've left us. There will be another big deadline in 30 days," Perdue offered.
The deal passed by Congress would boost the top 35 percent income tax rate to 39.6 percent for incomes exceeding $400,000 for individuals and $450,000 for couples, while continuing decade-old income tax cuts for everyone else.
Passage came nearly 24 hours after a decade's worth of tax cuts enjoyed by tens of millions of Americans expired with the stroke of the new year, technically raising taxes by more than $500 billion in 2013 alone.
But both Democrats and Republicans lamented their failure to reach a significant deficit-cutting agreement - setting up more showdowns between the two sides in the coming months. Perdue Wednesday called that unfortunate.
"It just points to the fact that this Congress, from my perspective, has been very inept and very unwilling to stand up. Americans, regular Americans, regular voters, all of us out here, need to demand more from the people we send to Washington to address the long term needs of the people of America," said Perdue.
Also weighing in were the authors of an influential bipartisan deficit-cutting proposal, former GOP Sen. Alan Simpson and Democrat Erskine Bowles, a former White House chief of staff under President Bill Clinton and former UNC system president.
They're now with the group Fix the Debt , and called the vote a missed opportunity.
"Washington missed this magic moment to do something big to reduce the deficit, reform our tax code, and fix our entitlement programs," said Bowles and Simpson in a joint statement.
"Our leaders must now have the courage to reform our tax code and entitlement programs such that we stabilize our debt and put it on a downward path as a percent of the economy."
Overall, the legislation passed Tuesday would add nearly $4 trillion to federal deficits over the next decade compared with what would have happened had all the tax cuts expired, according to the nonpartisan Congressional Budget Office.
Now, there will be more deficit cutting showdowns over the next three months, beginning when the government's legal ability to borrow money will expire and temporary financing for federal agency budgets will expire. Republicans have already said that, as they did in 2011, they will demand spending cuts as a condition for extending the debt ceiling.
"Congress has assured that there will be more embarrassing and damaging melodrama over the debt ceiling and spending in just a couple of months. I have held my nose and voted 'yes' many times, but this bill makes mindless cuts to programs important to the middle class inevitable," offered North Carolina U.S. Representative Brad Miller (D) District 13 in a statement after the vote.
Congressman Mike McInture, (D) District 7, said he voted against the compromise because it failed to solve the larger issues.
"The financial markets, small business and the American people are looking for stability and accountability, not a temporary fix. A comprehensive solution is needed that includes getting our national debt under control and reining in government spending," he said in a statement.
But Senator Richard Burr (R) said he voted yes because while the deal was "far from perfect," it prevented a tax increase on 99 percent of Americans.
"I supported this proposal because it protects 99% of Americans from increased taxes, it provides permanent certainty on the estate tax and Alternative Minimum Tax, it provides one year of protection for the reimbursement of doctors, it extends unemployment insurance for one year, and the net result of the deal provides over $600 billion that should be used to pay down our national debt," he said.
AP reporters Alan Fram, David Espo, Charles Babington, Andrew Taylor and Larry Margasak contributed to this report.