The US government took one step back from self-inflicted economic disaster on Tuesday.

House Republicans avoided the first attempt at assault by hardline conservatives, who are appalled at the bipartisan plan to suspend the debt ceiling until after the presidential election.

Many of the hardliners aren't buying into the mirage that the deal to cut some spending for two years and seek to control it after that will have a meaningful effect on the size and scope of the federal deficit.

Accomplishing that larger goal would require meddling with the sacred cows of American government spending -- from the Pentagon, Social Security and Medicare -- which weren't even part of this debt ceiling conversation.

President Joe Biden and House Speaker Kevin McCarthy have portrayed the debt ceiling bill as the best possible compromise achievable in the limited time before the Treasury Department is unable to meet its obligations, which could be as soon as June 5. And that could be, but it's not coming without objections from the political left and right.

Bill passes first test but House math is a moving target

A key conservative, Rep. Thomas Massie of Kentucky, broke with two other hardliners on the Rules Committee to vote with McCarthy-aligned Republicans to pass the bill through the committee. Even if he ultimately opposes the deal, Massie argued the full House should have the opportunity to weigh in.

The debt is a motivating issue for Massie. He frequently wears a home-made real-time digital debt clock on his suit so that anyone who talks to him has to see the trillions of dollars stacking up.

But his decision to vote to let the bill go to the floor means the debt deal could pass through the House Wednesday, even if it needs help from the many Democrats who seem likely to support it.

It's not clear how many Republicans will defy McCarthy and how many Democrats the minority leader, Hakeem Jeffries, can bring on board to make up the difference. Democrats said they expect Republicans to deliver the majority -- at least 150 of the 218 votes needed for passage.

House progressives are divided over the deal. "President Biden quite frankly kicked McCarthy's butt in negotiations. They wanted much more than they got; the president made sure they didn't get those things. But it's still a bad deal," New York Rep. Jamaal Bowman, who hasn't decided how he'll vote, told CNN's Manu Raju on Tuesday.

In the Senate, Minority Leader Mitch McConnell has backed the bill, signaling that -- barring unforeseen circumstances -- the deal could ultimately pass the chamber.

This will not fix the deficit

While the bill at hand will accomplish the important task of neutralizing the debt ceiling as a bargaining chip, it is not designed to do much of substance about controlling the spending that created the debt in the first place.

Lawmakers exempted spending on Social Security, which currently accounts for 19% of US spending; Medicare, 12% of spending; and national defense, 12% of spending, from the talks. Republicans rejected any suggestion of tax hikes.

Related: Where the government money goes

The social safety net and national security are drivers of the deficit lifestyle that has created the $31.4 trillion national debt. They would have to be on the table to truly contain spending.

According to a Congressional Budget Office analysis released Tuesday night, the bill would reduce budget deficits by $1.5 trillion over a decade. By contrast, the debt limit legislation passed by House Republicans in late April would have cut deficits by $4.8 trillion, according to the agency.

But CBO's score presents a potential problem for McCarthy. The work requirements provisions in the package would boost enrollment in the food stamps program by 78,000 people in an average month when fully implemented, as well as increase spending by $2.1 billion over the decade.

A spit over what should be on the table

CNN's Jake Tapper asked a Democrat -- Rep. Jason Crow -- and a Republican -- Rep. Ken Buck -- who represent very different viewpoints from Colorado why defense spending was not just exempted from cuts but will see an increase.

"I do not think it's a good idea to freeze everything else, but allow increases in the defense budget," said Crow. But he added, "Democrats do not control the House of Representatives right now. Republicans do. They have established that as a red line, and we're trying to negotiate as best we can to prevent a national default."

Buck, who said he will oppose the debt deal, wants to see both social spending and defense spending on the table.

"There is a lot of fat at the Department of Defense that we can cut," he told Tapper. "Procurement process and other areas we should be looking at very hard."

There is a growing divide in the GOP between hardline fiscal conservatives and those who want to protect defense and social spending.

Protecting Medicare and Social Security has been the blood oath of Democrats, who have long tried to motivate voters with accusations that Republicans are trying to take those social programs away.

This year, however, it is Republican presidential candidates like Florida Gov. Ron DeSantis and former President Donald Trump who are trying to outdo each other with pledges to protect that spending.

Trump, who enjoys enormous sway with House Republicans, had encouraged negotiators to hold out for as much in the way of cuts as possible and even suggested a debt default would be no big deal. McCarthy talked to him about negotiations in the days before the deal was announced, but Trump has been noticeably silent about it.

DeSantis, meanwhile, slammed it. And after his first official campaign event on Tuesday, the Florida governor called on Trump to take a position.

"I mean, are you leading from the front or are you waiting for polls to tell you what position to take?" DeSantis told reporters following his remarks in Iowa.

McCarthy could face a reckoning

Anger over the deal could have repercussions within the GOP generally and for McCarthy personally.

As he tried to secure the gavel in January, he agreed to give any member the power to challenge his position as speaker. That could mean angry hardline conservatives like Rep. Dan Bishop of North Carolina.

"None. Zero," Bishop told CNN's Manu Raju when he asked if Bishop had any confidence in the speaker. "What basis is there for confidence? You cannot forfeit the tool of Republican unity."

The political arm of the conservative Heritage Foundation announced it would penalize Republicans who vote for the deal.

"This debt ceiling deal does little to get at the root problems that have led to nearly $32 trillion in debt," it said in a statement.

But that is exactly the problem of using the debt ceiling as leverage to control spending, according to Democrats. It creates a desperate situation.

"Why is there a hostage situation where the American economy has been taken hostage in the first place?" asked Rep. Gregorio Casar, a progressive Democrat from Texas, during an appearance on CNN. "Why is the president having to make any sort of ransom payment?"

Related: These companies are winners in the debt ceiling deal

We've seen versions of this movie before

If controlling the debt were easy, lawmakers would have done it already. CNN's Tami Luhby has an excellent flashback to 2011, the last time there was a near default, when then-President Barack Obama, a Democrat, and then-House Speaker John Boehner, a Republican, were in power.

Congress hatched a plan to enact painful cuts -- known as sequestration -- as a sort of incentive to push legislators to unite behind a "big deal" to control spending. When the big deal fell through, lawmakers spent years unraveling the painful cuts.

Most people aren't opposed to cuts. At least not in theory.

The vast majority of the country (84%) wants the debt ceiling raised, according to a CNN poll conducted by SSRS and released last week, before a deal was announced. Only a small minority -- 15% -- of Americans said Congress should not do so under any circumstances. The 60% who said a debt ceiling hike should come with spending cuts might find something to like in this deal.

And the poll suggests the country may be less overtly partisan and more moderate than the sniping of its politicians often makes it seem. A larger portion -- 41% -- classify themselves as independents or members of another party rather than Republicans (30%) or Democrats (29%).

Those are relatively abstract questions. Opinions will be scrambled when lawmakers get around to the kind of across-the-board discussion that includes social spending, defense spending and tax rates that could have a real impact on the deficit.