The new bipartisan budget deal will be approved by Congress, but not everyone is going to be happy about it, Rep. Tom Cole, R-Okla., predicted Wednesday.
This agreement could not have happened "without people willing to accept less than they would like," Cole told CNBC's "Squawk Box."
The two-year budget framework—which includes $63 billion of sequester spending cut relief and $85 billion of total savings—now goes to the full House and Senate for consideration. The House is likely to vote by Friday, before recessing for the year, with a Senate vote to follow.
(Read more: US lawmakers announce compromise budget deal)
"As soon as I saw the numbers on what the agreement was, I said, 'Are you kidding me? That's it,'" investor Dennis Gartman reflected.
"I don't think that the stock market is going to take that very well at all. And it's not. It's just ho-humming it," the founder of The Gartman Letter explained on "Squawk Box" Wednesday.
Approval of the deal would avoid a government closure in January. The temporary deal that ended the October shutdown provided for funding for federal operations until Jan. 15, and an extension of the debt ceiling authority until Feb. 7.
"There's a lot to be happy with here: Government stability, the securing of the sequester cuts [and] the redistribution of that money in a more reasonable way that protects defense," the Oklahoma Republican Cole said.
"They came at a cost, and each side has some things to be disappointed about," he continued, but said that in his view "it will pass."
House Majority Leader Eric Cantor told CNBC's Larry Kudlow Tuesday night that the GOP leadership supports the budget deal progress, but not all Republicans are on board. Sen. Marco Rubio of Florida said he would not support the deal. Conservative interest groups such as Heritage Action and Americans for Prosperity are also urging Republicans to oppose it.
(Read more: Cantor: Budget deal 'maintains savings')
Despite Rep. Cole's confidence, the deal will be a tough sell in Republican-controlled House, argued Jim Nussle, former director of the Office of Management and Budget under President George W. Bush.
"After three years of nothing, they agreed to spend $63 billion more and pay for it later. Wow, no wonder its bipartisan," Nussle told CNBC Wednesday. The deal accomplished nothing, he said, and the optimism surrounding it proves that "a thirsty man will drink just about anything."
Roger Altman, deputy Treasury secretary during the Clinton administration, saw the deal as a step in the right direction—saying the spend more, pay later approach will provide a "little push" to the economy because growth is still weak. "It restores budget order," he said.
Both Altman and Nussle—who appeared together on "Squawk Box"—did agree that the agreement does nothing to address the long-term deficit problems, which can't be solved without entitlement reform.
The bitter partisanship in Washington has not only taken its toll on how Americans feel about Congress. President Barack Obama's approval rating stands at just 43 percent, according to a new NBC News/Wall Street Journal poll. Fifty-four percent disapprove of the president's performance—the highest proportion of his presidency.
(Read more: Obama has suffered damage in second term: Poll)
But Altman said he believes the new budget deal can help restore some of that lost confidence: "From the point of view of the business community and the investment community at large, it shows that government can do something when most people thought government couldn't."
—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.