President Trump inked a road map with Mexico, and — contrary to some media carping otherwise — he did win, at least on paper, some significant concessions from the nation’s southern neighbor.

Now the pressure is on both him and Mexico to show they can turn the tide with the changes, including more Mexican police patrolling that country’s southern border region and more Central Americans who cross into the U.S. being sent back to Mexico.

In Washington, Republicans called the president’s deal, struck late Friday, a masterstroke of negotiations. Mr. Trump had threatened to impose crippling economic tariffs on Mexico unless it agreed to make major changes, and that brought the foreign minister rushing to Washington to reach a deal, in writing, with the Trump administration.

“Mexico was not being cooperative on the Border in things we had, or didn’t have, and now I have full confidence, especially after speaking to their President yesterday, that they will be very cooperative and want to get the job properly done,” Mr. Trump tweeted Sunday.

Mexico now has 90 days to prove that its concessions can work, or else it will have to do more, the U.S. says. Mr. Trump, again on Twitter, signaled that he would be happy to renew his tariffs threat, and he even seemed a bit put out that he didn’t get to follow through on it this week.

The Trump administration had been careful not to set any concrete goals, so judging success will be tricky.

In May, more than 144,000 illegal immigrants were snared at the border and more than 100,000 of them were children or families — shattering records dating back decades. Homeland Security officials predicted the overall numbers would remain above 100,000 for months into the future, so one definition of success could be cutting those numbers below that mark.

Mexico’s ambassador to the U.S. offered an even more ambitious goal Sunday.

“What we talked was that the numbers have to go down like to previous levels that we had maybe last year,” Ambassador Marta Barcena Coqui told CBS’s “Face the Nation” program, saying they would like to see results “in a very relative short term, like in a month or a month and a half.”

In 2018, an average of about 50,000 people were snared at the border each month, meaning Mexico would have to achieve a reduction of nearly two-thirds of the flow in order to meet that target.

She said some of the technical details will be worked out over the next months, but Mexico did agree to deploy some 6,000 more national police to enhance security in its own southern border region — including policing illegal immigration.

Mexico also agreed to expand its cooperation with the Trump administration’s Migration Protection Protocols, the “remain in Mexico” policy under which the U.S. government is returning Central American asylum seekers to Mexico to wait while their cases are heard in U.S. immigration courts.

The goal is to change the incentive structure. Central Americans generally want to reach the U.S. and make asylum claims as a way of gaining a foothold. Few will qualify, but they can disappear into the shadows once on U.S. soil.

U.S. officials hope they lose the incentive to make the journey if they are made to wait in Mexico.

A smaller version of the Migration Protection Protocols has been in effect for months, but under the new deal, Mexico agreed to expand its cooperation borderwide. It will offer work permits, health care and humanitarian assistance to the migrants who are waiting on Mexican territory.

The U.S. agreed to speed up hearing asylum cases in U.S. immigration courts.

That was a lopsided deal in favor of the U.S., Republicans said.

“In general, Republicans understand tariffs are attacks on American consumers, and we don’t want to see them in place long term, nor do I believe President Trump does, either,” Sen. Ron Johnson, Wisconsin Republican and chairman of the Senate Homeland Security Committee, told “Fox News Sunday.” “He’s using tariffs as leverage in trade negotiations, and I think he used them as leverage in this situation brilliantly, quite honestly.”

Democrats were conflicted in their reactions.

Senate Minority Leader Charles E. Schumer, New York Democrat, first mocked Mr. Trump, saying — seemingly with as much sarcasm as can drip on Twitter — that since the deal was struck, Mr. Trump can stop talking about illegal immigration.

“I’m sure we won’t be hearing any more about it in the future,” Mr. Schumer tweeted Friday night.

By Saturday, though, Mr. Schumer said the president went wobbly and settled for offers that won’t work.

“Just as I predicted, the president backed off,” the New York Democrat said, doubting the president won anything of significance. “It is likely to have only a small impact on solving the root causes of Central American migration because many of the components are things Mexico is already doing.”

House Speaker Nancy Pelosi, California Democrat, feared Mr. Trump will be successful.

She said she feared migrants’ rights will be violated if they are made to wait in Mexico while their asylum cases are heard.

Democrats’ presidential candidates sided more with Mr. Schumer — and with media reports in The New York Times — in claiming that Mexico agreed months earlier to most of the steps being taken and that Mr. Trump’s victory lap was overblown.

“I think what the president has done is what, in fact, in many respects, Mexico has agreed to do many months ago,” Sen. Bernard Sanders of Vermont said on CNN’s “State of the Union.” “But 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.”

But Mexican and U.S. officials said the agreement goes beyond any previous deals, expanding Mexico’s cooperation with the Migration Protection Protocols and setting a framework for further cooperation.

“This is the first time we’ve heard anything like this kind of number of law enforcement being deployed in Mexico to address migrations,” acting Homeland Security Secretary Kevin McAleenan said on “Fox News Sunday.”

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