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')