Outgoing Senate Budget Committee Chairman Kent Conrad (D-N.D.) said Sunday that Congress should take one more shot at a big deal on the "fiscal cliff" before looking at President Obama's scaled-down package.

Sen. Kent Conrad (Nicholas Kamm/AFP/Getty Images)

“This is an opportunity to do something hugely important for the country,” Conrad said on "Fox News Sunday." “I would hope that we would have one last attempt here to do what everyone knows needs to be done – to get a larger plan that really does stabilize the debt and gets us moving in the right direction.”

Conrad urged the two sides to split the difference between Obama's last big proposal and House Speaker John Boehner's (R-Ohio) -- a package that would lead to $2.6 trillion in savings.

Asked whether he thought Obama’s plan was insufficient, Conrad said, “It may come to that.”

Meanwhile, Sen. John Barrasso (R-Wyo.) said Obama has made a cynical political calculation that going over the cliff without a big deal will work in his favor.

“I think the president is eager to go over the cliff for political purposes,” Barrasso said, adding: “He senses a victory at the bottom of the cliff.”