A stronger-than-expected September jobs report has pushed Wall Street's debate over how deeply the Federal Reserve will cut interest rates at its November meeting in favor of a more modest path.

Some have even suggested the report could mean the Fed won't cut rates at all next month.

"Looking at the labour market strength evident in September’s employment report, the real debate at the Fed should be about whether to loosen monetary policy at all," Capital Economics chief North America economist Paul Ashworth wrote in a note to clients on Friday. "Any hopes of a [50 basis point] cut are long gone."

As of Friday morning following the jobs report's release, markets were pricing in a roughly 8% chance the Fed cuts interest rates by half a percentage point in November, down from a 53% chance seen a week ago, per the CME FedWatch Tool.

EY chief economist Gregory Daco wrote in a note to clients that the report should "bolster the view among Fed officials that there is no rush to cut interest rates." He added that some officials "may even lean in favor of a pause."

Entering Friday's print, markets had been heavily debating whether the central bank would need to enact another jumbo-sized interest rate cut at its next meeting amid signs of slowing in the labor market. In addition to price stability, achieving maximum employment is part of the Fed's mandate.

But Friday's report countered any signs of slowing across a variety of metrics. Data from the Bureau of Labor Statistics released Friday showed the labor market added 254,000 payrolls in September, more additions than the 150,000 expected by economists. Revisions to both the July and August report showed the US economy added 72,000 more jobs during those two months than previously reported.

Meanwhile, the unemployment rate the unemployment rate fell to 4.1%, from 4.2% in August.

The data fit the narrative Fed Chair Powell laid out in his most recent press conference on Sep.18 when he said the labor market is "actually in solid condition."

"The US economy is in good shape," Powell said. "It's growing at a solid pace. Inflation is coming down. The labor market is in a strong place. We want to keep it there. That's what we're doing [by cutting interest rates]."

Nationwide chief economist Kathy Bostjancic and many other economists still believe the Fed will cut interest rates by a quarter percentage point twice more this year as the central bank forecasted in its most recent Summary of Economic Projections (SEP).