The unemployment rate edged up slightly in June—and weirdly, this might be good news.

According to the real estate giant Redfin, the soft jobs numbers could give the Federal Reserve a long-awaited excuse to cut interest rates as soon as September.

Economist says another key indicator will be last month's Consumer Price Index, which is due to be released on Thursday. Forecasts are pointing to 3.1%—still above the Fed's target of 2% but moving in the right direction.

"If that report comes in largely as expected, the Fed should be able to start laying the groundwork, perhaps as soon as their July 31st meeting, for rate cuts to start in September," Redfin economist Chen Zhao said.

Although she believes that there's still a possibility of a rate cut even if the CPI reading disappoints, "it would feel aggressive in the context of a labor market that's not yet weak."

The Federal Open Market Committee has struck a cautious tone when it comes to reducing rates from the current target range of 5.25% to 5.5%, which has been in place for a year.

By kicking the can down the road until September, FOMC members would be able to see how the next three inflation reports are shaping up—offering further evidence that inflation is cooling as hoped.

Zhao said last week's jobs numbers were especially promising because they show the labor market is softening without the prospect of an imminent recession.

What it means for the housing market

With borrowing costs, chief among them mortgage payments, at multi-decade highs, Americans are paying much closer attention to interest rate projections than they used to.

While Zhao believes that rates will fall between now and the end of the year, she went on to strike a note of caution.

"We are still living in a world of elevated uncertainty as expectations around Fed policy may change quickly depending on each month's inflation data and the increasingly turbulent road to the November U.S. presidential election," she warned.

Freddie Mac's chief economist, Sam Khater, agrees.

"We are still expecting rates to moderately decrease in the second half of the year, and given additional inventory, price growth should temper, boding well for interested homebuyers," he said.

Will that help fix the housing affordability crisis? Analysts aren't so sure.

Bank of America recently warned that a "lock-in effect" could persist for years because homeowners secured rock-bottom fixed-mortgage rayes when they were below 3%.

That means it may take a much bigger drop in rates to set loose homeowners who are essentially "trapped" in their current properties, unwilling to trade in their locked-in rates.