Representative Steve Pearce, a New Mexico Republican, asked Ms. Yellen rather incredulously at a congressional hearing in February whether the Fed would really try to offset faster growth by raising rates more quickly. Ms. Yellen’s response was carefully couched, but it amounted to “yes.”

She said the Fed was fine with faster growth so long as it reflected an improvement in economic fundamentals. On the other hand, she said, the Fed would try to offset faster growth “if we think that it is demand-based and threatens our inflation objective” — a technical description of what would happen if Congress cut taxes or increased spending.

The White House and the Fed have very different economic outlooks.

Mr. Trump has repeatedly painted economic conditions in some of the bleakest language ever used by an American president, and he has described his fiscal policy agenda as necessary to revive growth and restore the nation’s prosperity.

Gary Cohn, the head of the president’s National Economic Council, told CNBC on Friday that he expected job growth to strengthen in the coming months.

“We’re very excited about what’s ahead of us,” he said.

Fed officials, by contrast, see the pace of job growth as unsustainable. The unemployment rate fell below 5 percent last May. Since then, employment has continued to expand at an average of 215,000 jobs a month — more than twice the job growth necessary to keep pace with population growth. The faster growth is good news for the economy, indicating that adults who gave up on finding jobs are returning to work. The question is how long that can continue.

There are already growing signs of a tighter labor market. The Federal Reserve Bank of Dallas recently reported that Texas employment in residential construction had nearly reached the level seen before the 2008 financial crisis and that skilled workers like framers, masons and bricklayers were in short supply. Average hourly earnings, adjusting for inflation, climbed 20.3 percent in the Texas construction sector from 2011 to 2016, compared with 5.9 percent for all Texans in private-sector jobs, the Dallas Fed reported. The National Association of Homebuilders reported that 82 percent of builders regarded the cost and availability of labor as their primary concern.

The Fed’s slow march toward higher interest rates is gradually raising borrowing costs for businesses and consumers. The average rate on a 30-year mortgage loan was 4.21 percent last week, up about half a percentage point from the same time last year, according to Freddie Mac. Rates on credit cards and car loans have also ticked higher, although borrowing costs remain well below historical norms.