Consumers are tired of inflation. But some retailers fear falling prices

Just ahead of the holiday season, Walmart had encouraging news for inflation-weary shoppers: Prices on food and other staples were falling instead of rising. The retail giant said if the trend continued, it would soon contend with deflation in some of those key household categories, which would be a welcome sight for consumers emerging from the worst price increases in decades.

But the retail giant backpedaled this week, saying higher prices on many grocery items and household staples like paper goods have stuck.

"There is deflation in certain categories — the possibility overall still remains — but prices are more stable than where they were three months ago," CFO John David Rainey told CNBC.

In recent weeks, corporate leaders have sung a similar tune — at a time when inflation is cooling but prices are still rising faster than the Federal Reserve would like. Home Depot said the prices of home improvement items have "settled" rather than fallen. Coca-Cola and the makers of other popular brands of snacks, sodas and household essentials said their prices are still ticking higher than a year ago. While they're planning for more modest price hikes, shoppers should not expect price cuts, either.

"If one looks at inflation over time, we very rarely get into periods of sustained deflation. That's just not a consumer effect," Coke CEO James Quincey said Feb. 13 on CNBC's "Squawk on the Street."

The latest government data backs that up: while the rate of price increase is dipping year over year, the latest inflation metric came in hotter than expected. The consumer price index, a broad measure used to track what shoppers pay for goods and services across the economy, rose 3.1% in January from the prior year.

Food prices climbed 2.6%,