The Federal Reserve's push to bring inflation down to 2% is likely to cause a spike in job losses and tip the U.S. into recession — the only question is how deep, billionaire investors said in the aftermath of the latest interest rate hikes.

Carlyle Group co-founder David Rubenstein said on CNBC this week that the unemployment rate could jump to 5% or 6% based on Fed Chairman Jerome Powell's warning of pain in the name of cooling inflation.

"Probably something between a hard landing and a modestly hard landing is what they would like," he said.

The Fed raised interest rates again on Wednesday by 0.75 percentage points after the latest consumer price index statistics showed inflation growing 8.3% year-over-year in August. The median projection for the federal funds rate by the end of the year is between 4.25% and 4.5%, higher than a path previously set by the Fed this summer.

“We want to act aggressively now and get this job done and continue to act until we get it done,” Powell said at a press conference Wednesday.

Starwood Capital Group CEO Barry Sternlicht also went on CNBC recently and said the Fed is being too aggressive on raising rates. Sternlicht said the Fed's actions are already having a major impact and that it should target inflation at around 3% to 4%.

"They’re attacking the economy with a sledgehammer, and they don’t need to," Sternlicht told CNBC's Squawk Box last week, as reported by CoStar. “The pace of rent increases, we’re seeing it go down in month to month, not year over year. ... You’re going to see the rent component of CPI continue to rise because it’s such old data they have.”

DoubleLine Capital CEO Jeffrey Gundlach said with the bond market showing an inverted yield curve, he thinks a recession is imminent and the Fed has moved too aggressively.

“I do think we’re headed to a recession, and I think the Fed should have pasted this differently,” Gundlach said on CNBC Wednesday. “We've been tightening now for a while. And the impact of these tightenings is going to cumulate into a recession ... I do think the Fed should be slowing down on these rate hikes.”