Amid signs of a weakening labor market, the Federal Reserve now finds itself in a bind: If it cuts interest rates too soon, it could risk reigniting the price increases that have bedeviled the post-pandemic economy. But if it keeps rates elevated, the job security of millions of Americans could be further jeopardized.

The Consumer Price Index for the month of June, due to be released by the Bureau of Labor Statistics this morning at 8:30 a.m., is expected to offer further insight into the…