Deficit hawks insist that spending cuts are a priority and they are not impressed with the fiscal cliff deal signed into law Wednesday. The highly anticipated compromise prioritized taxes but failed to address the debt ceiling, presenting new risks as another deal needs to be hammered out.

The country's two best-known deficit hawks — Erskine Bowles and Alan Simpson — called the latest deal “a missed opportunity,” CNNMoney reports.

“In fact, Washington politicians set up [the fiscal cliff] to force themselves to seriously deal with our nation's long term fiscal problems. Yet even after taking the country to the brink of economic disaster, Washington still could not forge a common sense bipartisan consensus on a plan that stabilizes the debt," Bowles and Simpson said in a statement.

Video: Economist Predicts 'Unthinkable' for 2013 

Had this week's deal not been reached, scheduled tax hikes and spending cuts threatened to drag the economy into a serious recession.

But, Rudolph Penner, former director of the Congressional Budget Office, told CNNMoney that Congress and the White House “didn't do much else.”

“And they gave us a New Year's Eve present of another cliff in two months,” he noted.

Under the compromise, the spending cuts, which were considered so potentially devastating, are only postponed until March 1. This gives lawmakers a two-month extension to reach an agreement on how to reduce the deficit.

That fiscal cliff deadline will be followed by another on March 31, when temporary legislation to keep the government running is set to expire. Looming over both of those cutoffs is the even more contentious question of raising the nation's debt ceiling of $16.4 trillion, The Washington Times explained.

The United States has already reached its borrowing limit, but the Treasury Department is employing “extraordinary measures” to keep the government running for now. If Congress refuses to play nicely and raise the debt ceiling, the government could start defaulting on its bills in the near future.

This brings spending cuts back to the fore, and some Republicans are calling for unwavering hardball this go-round.

“We Republicans need to tolerate a temporary, partial government shutdown,” Sen. Patrick Toomey, R-Penn., told MSNBC. “It's disruptive, but it's a hell of a lot better than the path we're on. We absolutely have to have this fight over the debt limit.”

Video: Economist Predicts 'Unthinkable' for 2013