Kevin M. Warsh cleared a crucial hurdle at his first appearance as the Federal Reserve’s chairman at its annual conference in Jackson, Wyo. He offered his most comprehensive views to date about the state of the economy.

He cleared up confusion about the central bank’s commitment to getting inflation down to its 2 percent target after sending mixed messages the month prior. And he acknowledged that the Fed might have “work to do” to make good on that pledge, suggesting a readiness to raise interest rates if price pressures do not ease. But the path ahead for Mr. Warsh is a precarious one.

Financial markets now see a quarter-point increase at the central bank’s next meeting on Sept. 15-16 as more likely than not, leaving Mr. Warsh with a tough decision whether to follow through with action. Another month of benign inflation data will alleviate the pressure on him to raise rates in September. But as the market blowback to his last meeting in July showed, the onus will be on him to explain how doing nothing aligns with his intolerance for elevated inflation.

A rate increase next month would help to underpin the seriousness around Mr. Warsh’s inflation pledge. Delivering that just before midterm elections, however, would create an immediate showdown with the Trump administration. “He has multiple targets on his back,” Maurice Obstfeld, a senior fellow at the Peterson Institute for International Economics and former chief economist at the International Monetary Fund, said on the sidelines of the conference. “It’s a no-win situation.