TWO DOMESTIC concerns towered above all others as President Obama addressed a joint session of Congress on Tuesday night on the state of the union. One was stubbornly slow economic growth. The other was the long-term threat to prosperity posed by the structural mismatch between the federal government’s projected revenue and its spending commitments. A successful second term for Mr. Obama will require both credible proposals for overcoming those related challenges and the determination to carry them through.

The president addressed the deficit and debt first, and at some length. This was fitting, giving that the most pressing piece of business facing Washington is what to do about the impending $85 billion across-the-board spending cut. He was forthright in declaring that this so-called sequester threatens the military as well as domestic programs. But his plan to avoid it basically repeated the offer of a “balanced approach” — unspecified tax hikes and spending cuts — which Republicans have already rejected.

Somewhat more substantively, he called for a larger deficit-reduction deal built around loophole-closing tax reform and what he called “modest” reforms to Medicare and entitlements. In an apparent effort to rally Democrats to this cause, he called on “those of us who care deeply about programs like Medicare” to “embrace” reform.

Yet in promising the same amount of Medicare savings as the Simpson-Bowles commision proposed, Mr. Obama did not mention that this would be a mere $341 billion over 10 years. All told, he envisions shaving an additional $1.5 trillion off projected deficits over 10 years, which would leave the national debt at a historically aberrant 70-odd percent of gross domestic product. In short, he declined to push back against the mind-set within his party that considers acceptable “stabilizing” the debt at this level by the time Mr. Obama’s second term ends. At best, that would buy a respite of a few years before the debt resumed its upward climb.

As for raising the economy’s growth potential, the president was more persuasive. His emphasis on reforming the tangled and counterproductive corporate tax code was especially welcome, and relatively likely to draw GOP support. He offered several promising ideas on education, including a promise of “high-quality preschool” for all children, though how that would square with his promise not to increase the deficit by a single dime went unexplained. He sounded a ringing call for greater federal attention to college cost containment. “Taxpayers can’t keep on subsidizing” spiraling tuition, he said, candidly and correctly.

As European trading partners had hoped, the president endorsed negotiations for a transatlantic free-trade zone, which would help America’s export industries and the jobs that depend on them. Coupled with an agreement that Obama is promoting for the Pacific region, the proposal has the potential to make his second term fruitful for global trade. He also suggested raising the federal minimum wage, from $7.25 per hour to $9 — although the precise amount is less important, in our view, than the president’s call for annual cost-of-living adjustments.

In keeping with Mr. Obama’s theme of nation-building at home, foreign policy played a secondary role in his speech. He promised to bring home half of the remaining U.S. troops in Afghanistan within the next year. But officials said the withdrawal would be weighted toward year’s end, leaving most of the troops to partner with Afghan troops for much of this year. The president said the United States would support democratic transitions in the Middle East, “keep the pressure on [the] Syrian regime” and “do what is necessary to prevent” Iran from obtaining a nuclear weapon — but he offered no specifics.

Mr. Obama pressed his case for reform of immigration laws and for action to slow global warming — and, in especially moving terms, tougher gun laws. In each case, there may be measures he can take through executive action, but new laws will be needed for substantial progress.

Mr. Obama was right when he pointed to the survivors and grieving relatives of gun violence victims and insisted, “They deserve a vote.”