WASHINGTON — Investors in financial markets, and those predicting faster economic growth in 2017, would do well to remember the famous words that William McChesney Martin Jr., the former Federal Reserve chairman, uttered way back in 1955: The Fed’s job is to remove the punch bowl just as the party gets going.

President-elect Donald J. Trump’s promises to cut taxes and regulation and to increase spending on infrastructure and defense have convinced many that a sugar high in the near term will goose the economy. But Fed officials say the economy is already expanding at something close to its maximum sustainable pace, meaning faster growth would drive inflation toward unwelcome levels.

To avoid overheating, the Fed could respond by raising interest rates more quickly. The more Mr. Trump stimulates growth, the faster the Fed is likely to increase rates.

“I guess I would argue that I think people have gotten a bit ahead of themselves about what a Trump presidency would mean,” said Lewis Alexander, chief United States economist at Nomura. “If we have a big stimulus, the logical thing for the Fed to do is to raise rates faster. There isn’t a whole heck of a lot of scope to just let the economy run under those circumstances. There’s a big question about whether fiscal stimulus under Trump just leads to higher interest rates.”