The Federal Reserve was already facing a tough decision about how quickly to lower interest rates after restarting cuts last month. But that judgment call is set to get much harder if the government shutdown deprives the central bank of essential data points that help it gauge the state of the economy.

The Bureau of Labor Statistics has said it would not publish Friday’s hotly anticipated jobs report. Other key data releases, including the next Consumer Price Index report, are also in peril if Congress and President Trump do not reach a deal soon.

That would leave the Fed with a murky view of the economy when the central bank’s officials are already at odds about its approach to interest rate cuts before their next vote at the end of the month.

“It pains me that we wouldn’t be getting official statistics at exactly a moment when we’re trying to figure out is the economy in transition,” said Austan Goolsbee, president of the Federal Reserve Bank of Chicago and a voting member on this year policy-setting committee.

What policymakers would like to know is just how much they are restraining the economy with their policy settings. That assessment gets harder if they have only alternative sources of economic data to parse.

If interest rates are holding back growth only a little bit, the Fed may not have much room to reduce borrowing costs before reaching what officials refer to as a “neutral” level. That is one in which the Fed’s policy settings are neither hastening economic activity nor hindering it. Getting there too quickly, or overshooting that destination, would risk worsening inflationary pressures that have originated from Mr. Trump’s tariffs. But if interest rates are restraining growth significantly, policymakers might need to provide a lot of relief quickly or risk jeopardizing the labor market.