(CNN) President Donald Trump is blasting critics who claim his new border agreement with Mexico is a mirage rather than the huge victory he is claiming, as he rides into a fresh week of constitutional collisions with Democrats.

Trump unleashed a torrent of tweets and called into CNBC on Monday morning to proclaim the immigration deal as a triumph, argue that it would never have been achieved without his use of tariffs as a weapon and warn that China would also have to cave, addressing a separate economic duel.

Like many of Trump's wins, there are questions about whether the immigration deal adds up to real progress or is a contrived solution conjured up to get him out of yet another self-created crisis. His determination to politicize the issue is only adding to the doubts.

"If we didn't have tariffs, we wouldn't have made a deal with Mexico. We got everything we wanted," Trump said on CNBC, before adding that China, with which he is waging an escalating trade war, would not be able to stand the heat.

"Right now, China is getting absolutely decimated by companies that are leaving China, going to other countries, including our own, because they don't want to pay the tariffs," Trump said, without providing evidence for his claims.

Trump is also reacting angrily to suggestions that the Mexico agreement, concluded late Friday night, is just a new example of the alternative reality he often creates to sustain his presidency and will do little to solve the southern border emergency.

Controversy over the deal also reflects how a common definition of facts has become impossible under a President who has often sought to devalue the currency of truth.

"If President Obama made the deals that I have made, both at the Border and for the Economy, the Corrupt Media would be hailing them as Incredible, & a National Holiday would be immediately declared," Trump wrote on Twitter on Sunday.

"With me, despite our record setting Economy and all that I have done, no credit!"

If President Obama made the deals that I have made, both at the Border and for the Economy, the Corrupt Media would be hailing them as Incredible, & a National Holiday would be immediately declared. With me, despite our record setting Economy and all that I have done, no credit! — Donald J. Trump (@realDonaldTrump) June 9, 2019

The dispute over the President's claimed breakthrough comes with fraught relations between Trump and Democrats set to cross another rubicon.

The House is expected Tuesday to vote to hold Attorney General William Barr and ex-White House counsel Don McGahn in contempt, in a further escalation of a separation of powers duel

Jury out on Mexico deal

Democrats on Sunday pounced on a New York Times report that said that Friday's deal mainly includes pledges previously made by Mexico in talks with the United States in recent months.

But the President argued on Twitter that his intervention and threat of tariffs had been instrumental in getting the promises down on paper.

Controversy over the Mexico deal reflects how a common definition of facts has become impossible under a President who has often sought to devalue the currency of truth.

Perhaps in the weeks to come, the President's agreement, reached after exhaustive US-Mexico talks in Washington while he was in Europe last week, will turn out to be a significant breakthrough.

He argues that his threats of new tariffs forced Mexico into a more robust effort to stop the flow of migrants towards the US and will mitigate the southern border crisis that his administration has failed to control.

Conservatives are proclaiming the deal that staved off a building Republican revolt in the Senate as a media-confounding coup for the President's unpredictable art of the deal tactics.

In a Washington Post column, radio host Hugh Hewitt accused Trump's critics being no more able to "admit he played high-stakes poker and won a round on border security than they can admit that the president delivered a magnificent tribute to the heroes of Normandy on Thursday."

Trump stepped back from his threat to impose 5% tariffs on Mexico starting Monday that would have risen by 5% per month until they reached 25% after experiencing stiff pushback from GOP senators.

An alternative interpretation of the weekend's events — and Trump's furious propagandizing on Twitter — is that the deal with Mexico was mostly about saving presidential face.

If that is the case, the GOP is now closing ranks after senators did not hide their dismay at Trump's tariff threats — his dominant foreign policy tool — last week.

Missouri Sen. Roy Blunt — a self-admitted free trader and no fan of tariffs, even suggested Sunday that the drama could help resolve an even more complicated trade war against a foe that seems far less keen to accommodate Trump than Mexico.

"I think the biggest lesson here and biggest message here is now not to Mexico but to China," Blunt said on CBS "Face the Nation."

"The President is clearly willing to use tariffs and actually the President believes that tariffs are a significant, positive, economic tool."

It's not surprising that Trump faces widespread skepticism for his claims of victory, since he has a record of impulsively escalating crises, then 'solving' the problems he caused.

The President has hyped several trade deals, with South Korea, Canada and Mexico as full rewrites of existing pacts, but critics argue that he only secured cosmetic changes.

Last year, Trump proclaimed a huge new trade deal with the European Union after backing off his threats to impose new automobile tariffs. In fact, the two sides agreed to talk about an agreement that is still yet to materialize.

The President also repeatedly threatened to close the border with Mexico earlier this year if it failed to halt migrant flows, before backing down amid domestic criticism.

Trump had been warned that closing the border with Mexico, the third largest US trading partner, could cause an economic disaster for the US, hike prices Americans pay for staple products like fruit and vegetables and lead to shortages in supermarkets.

Trump claims on deal debunked

Given the paucity of detail about Friday's deal, it's hard to assess just how effective it might be.

The New York Times reported that Mexico's plan to deploy its National Guard — a far less potent force than its US equivalent — to stop migrants had already been agreed to in March. And an expansion of a program to keep asylum seekers in Mexico while their claims were processed had been announced in December, according to the paper.

Critics argued effectively that the President was trying to pull the wool over America's eyes and, far from highlighting his skills, exposed the futility of his approach.

"What the President has done is tout what, in fact, in many respects Mexico has agreed to do many months ago," Democratic White House hopeful Sen. Bernie Sanders said.

"I think what the world is tired of and what I am tired of is a president who consistently goes to war, verbal war with our allies, whether it is Mexico, whether it is Canada," Sanders said on CNN's "State of the Union."

Another Democratic candidate, former Texas Rep. Beto O'Rourke, said that Trump had "completely overblown what he reports to have achieved."

"They might have accelerated the timetable, but by and large the President achieved nothing except to jeopardize the most important trading relationship that the United States of America has," O'Rourke said on ABC News "This Week."

Friday's deal also does not appear to take aim at the root causes of the human exodus — violence and lawlessness in Central America — apart from vague wording on a greater US role.

Trump has already said he will cut hundreds of millions of dollars in aid to Honduras, El Salvador and Guatemala accusing them of doing nothing to stop the migrant crisis.

And Martha Bárcena Coqui, Mexico's ambassador to the US, refused to confirm Trump's tweeted claim that her government had agreed to immediately buy large quantities of products from "OUR GREAT PATRIOT FARMERS."

She said on "Face the Nation" simply that trade would increase in the absence of new tariffs and under the new US/Mexico/Canada deal — indirectly contradicting the President's tweet.

Either way, Trump has a 2020 card to play

In a political sense, it may not actually matter that much whether the deal with Mexico heralds a genuine breakthrough — a sign of the warped reality of the current political age.

The President has spent the weekend claiming victory, offering new material for his conservative cheerleaders and debunking criticism of his effort as evidence as media bias.

If in a few months the border crisis is eased, Trump can deservedly co-opt a new applause line at his campaign rallies and claim vindication for his hardline border policies.

He will claim that he has honored his predictions of a fix-it presidency that is racking up deals for the American people.

But if it becomes clear that the Mexican deal was a bust, Trump can return to the political well of border politics again in the knowledge that inflammatory rhetoric about migrants and attacks on Mexico feed the agitation in his political base he needs in 2020.

"We can always go back to our previous, very profitable, position of Tariffs - But I don't believe that will be necessary," Trump tweeted Sunday, accusing media outlets raising questions about the deal of wanting to see America fail.