Perhaps most significant, wage growth is also steady or slightly declining, rather than accelerating. Average hourly earnings for private-sector workers rose 0.2 percent in May, and are up 3.1 percent over the last year. Wages rose 3.4 percent in the year ended in February.

If this really were a situation of softening job growth because employers were up against the constraints of full employment, you would expect them to have to pay more to find scarce workers. Instead, the wage growth picture is steady as she goes.

Finally, all of that came before a major escalation of the trade wars that began in early May. The surveys on which the new data are based cover the middle of the month, so there is no reason to think employers would have changed their behavior in response to the latest headlines in time to affect these numbers. The trade war to date has already been damaging for sectors including automobile production and agriculture. And a cycle of higher tariffs on Chinese imports and retaliation against American exports could spread further in months ahead — not to mention a new round of tariffs threatened to go into effect on Mexico next week.

All these numbers don’t add up to a crisis, and there is no reason to assume that a recession is inevitable. But it does amount to the clearest evidence yet that the economic slowdown isn’t a figment of the bond market’s imagination, but something that is happening all around us, even if a few really good jobs reports in a row hid that fact.

The Fed and its chairman, Jerome Powell, will meet June 18-19. They are loath to appear to be responding only to what happens in the financial markets — their job is to try to watch out for the real economy, not treasury bond prices.

They are not in the easiest position. Their main interest rate target is quite low by historical standards, especially in the context of a decade-long expansion. There’s concern about having space to maneuver if the next recession hits. Still, the current federal funds rate of 2.25 to 2.5 percent leaves room to cut rates over the coming quarters to a degree that would cushion the economy.

And the soft May employment numbers offer an opportunity for the Fed to ground a policy pivot on conditions that affect ordinary Americans, not because bond investors expect that they will cut rates.

Both the market and the economic data are now suggesting that the Fed overtightened interest rates in 2018, and that the economy is at risk if it does not correct things. Mr. Powell and his colleagues are on the clock to decide what to do about it.