One could almost hear the sighs of relief — from the people who support President Donald Trump, and from some of those who oppose him, too.

They had just heard the president’s first speech before a joint session of Congress, and while the substance of it was largely consistent with his earlier pronouncements, there was an unmistakable change in tone.

For the first time Trump showed a significant effort to do outreach beyond his political base.

These joint-session speeches are always showpieces, regardless of who’s in the White House. The president and first lady followed the tradition of hosting guests, bringing in representatives of the country’s diverse population. An African-American student, with her success story. A disabled woman who benefited from a treatment, as testament to the potential of a less-regulated Food and Drug Administration to enable innovation.

Those were anecdotal expressions, and some critics within minority groups have reacted with raised eyebrows, saying it will take more than words to convince them that Trump’s administration will be inclusive.

But they were expressions nonetheless, and when it’s the president of the United States speaking, words do matter. Tone matters. All Americans should hope Trump absorbs the primarily positive reviews his speech received, and begin to favor that more presidential vernacular, in lieu of barbed tweets.

Those listening intently from across the political aisle, however, will require action rather than mere words, something that more plainly demonstrates a willingness to compromise in pursuit of common interests.

Specifically, the president will surely find that his budgetary goals, even as outlined in the brief proposal released this week, will be all but impossible to achieve without significant sacrifice.

At the same time as he’s exhorting other members of the NATO alliance to spend more on shared defense duties, Trump is pushing for a roughly 10 percent boost in the allocation for the U.S. military.

He has yet to explain how this money would be spent, beyond some distressing references to an expansion of the U.S. nuclear arsenal. Nor does he say how this comports with the military’s own acknowledgement of a need for better efficiency, or its longstanding evolution into a lighter and leaner 21st-century force.

Most importantly, he doesn’t explain how the projected cuts to domestic spending will play out, but they would have to be brutal to achieve the stated ends. The president has said repeatedly he opposes cutbacks to Medicare and Social Security, but entitlements are the largest cash bucket in the domestic budget.

Challenges in the nation’s schools, the problems of urban crime, the need for health care — all of these are complex issues that require resources. Nothing Trump has championed in recent weeks — neither charter schools, private prisons, nor his still-unspecified health-reform plan — comprise any kind of solution. They do not allay fears that progress will remain elusive in these areas.

The national security theme of his address, dominated by his determination to overhaul immigration policy, presents another question mark. Trump seemed open to considering a legal status for undocumented immigrants who have maintained a clean criminal record.

That provided a glimmer of hope that America’s paralysis on immigration could end, with bipartisan support. But unless there are concrete moves toward real negotiations with Congress, the prospects for comprehensive reform are dim.

The more conciliatory presentation in Tuesday’s speech came as a welcome surprise to Americans, who largely seem willing to take it at face value. The nation — the whole world — takes notice of presidential language.

But the listening is done, for now. It’s time to watch and see what he can deliver.