The compromise bill, agreed upon on Friday, had been an exercise of last-minute adds and changes to secure the votes of holdout and undecided Republican lawmakers. Republicans hold 52 of the 100 seats in the Senate, so they can't afford too many no votes from their members.

"This is one way that President Trump misplayed his hand. A couple of Democrats should have been for these tax cuts," Allen said on "Squawk Box." The revamped bill is expected to pass both chambers and signed by President Donald Trump before Christmas.

Republicans did not have to go it alone in their bid to deliver the most sweeping changes to the U.S. tax code since the Reagan-era 1986 overhaul, Axios Executive Editor Mike Allen told CNBC on Monday.

Republican Sens. Marco Rubio of Florida and Bob Corker of Tennessee moved into the yes camp late last week. Over the weekend, GOP Sens. Susan Collins of Maine and Mike Lee of Utah put out positives statements but stopped short of revealing whether they're ready to support the bill.

On Sunday, the office of Sen. John McCain said the Republican lawmaker returned home to Arizona after being hospitalized for side effects from chemotherapy treatment for brain cancer. He won't be in Washington to vote for the tax bill, but his absence is not expected to be crucial to the outcome.

Passage of tax reform, which features a federal corporate rate cut from 35 percent to 21 percent and reductions in taxes for many individuals, certainly would keep "Republicans in the game," heading into next year's midterm elections, Allen said.

Proponents see the bill as a big tax cut for companies and working Americans. But critics claim it's a giveaway to the rich with little relief for the middle class. Analysis from the tax-writing House Ways and Means Committee supports the former, while other forecasters such as the Joint Committee on Taxation were far less kind.

"If they did a belly-flop" on taxes, like GOP lawmakers did earlier this year when they failed to make good on seven years of promises to repeal Obamacare, they would be so "behind the curve" in their bid to maintain their margins of majority in the House, and more importantly the closely split Senate, Allen said.

However, Allen said Trump and Republican leaders on Capitol Hill could also have gotten some moderate Democrats, such as Sen. Joe Manchin of West Virginia, onboard if they had engaged the other side from the beginning.

"When you're giving stuff away, you should be able to get Democrats to join you," said Allen, formerly chief White House correspondent at Politico. "It would give this plan so much more insurance for the long run."

A bipartisan moment could have served Republicans well, he said, since they railed against former President Barack Obama and Democrats for passing the 2010 Affordable Care Act, better known as Obamacare, without any GOP support.