Fueled by a newfound consumer appreciation for value since the recession, Family Dollar is quickly expanding. Last year, the company opened 475 stores. Another 500 are set to open this year.
"We're in a business that's growing rapidly and while we are seeing pressure on our core customer, we're seeing other customers who weren't maybe shopping in the dollar channel moving into our dollar channel, and that's the fastest-growing segment of our customer base," Winston said.
Competitor Dollar Tree announced on Wednesday that it saw a traffic boost during the holiday quarter.
The average amount that shoppers spent per trip rose, and "record numbers" of customers shopped at the chain, said Bob Sasser, the company's chief executive.
Discounters Report Softness
Other discount retail chains, including Target and Wal-Mart, have already warned of signs of strain among consumers.
"As we enter 2013, we will plan appropriately as the U.S. economy is growing at a painfully slow rate and unemployment remains persistently high," said Gregg Steinhafel, Target's chairman, chief executive and president, during its earnings conference call. "While there are some encouraging signs in the housing market, volatility in consumer confidence, the payroll tax increase, and rise in the price of gas all present incremental headwinds."
(Read more: Target Earnings Top Forecasts, Despite Holiday Weakness)
To make matters worse, many retailers delivered especially strong sales numbers during the first quarter of 2012, which means they face tough comparisons ahead.
"Like some others that have reported, sales results have been softer than expected so far in February, and daily volatility has been elevated," said John Mulligan, Target's chief financial officer, on a conference call to discuss its latest results. "Yet trends have improved somewhat as the month has progressed, and it's still early in the quarter, so we believe our guidance is appropriate."
Last week, Target's larger rival Wal-Mart echoed this weakness in February, pinning the softness in large part due to delayed income tax returns.
"February sales started slower than planned, due in large part, to the delay in income tax refunds. We began seeing increased tax refund check activity late last week in our stores, resulting in a more normalized weekly sales pattern for this time of the year," Bill Simon, Walmart U.S. president and chief executive officer, said in a statement.
To counteract the delayed refunds and smaller paychecks, Walmart will be changing some package sizes and other store offerings to appeal to shoppers who have been hit by the tax hike.
Once these consumers receive their refunds, spending will improve somewhat, predicted Peter Keith, senior research analyst at Piper Jaffray.
"So ultimately you'll see a bit of a pickup in lower income spending, we think, as you get into March and the refund activity picks up a little bit," Keith told CNBC. "But the full-year outlook for the lower-income consumer is definitely a bit depressed compared to how it's been the last few years."
Overall, Dana Telsey, chief executive of the Telsey Advisory Group, said the month of February is definitely somewhat cautious so far for retailers.
"I think overall what we're learning is the month of February is definitely a little bit cautious," Telsey told CNBC on Wednesday. "We're seeing guidance come in below consensus numbers. First half of the year, it doesn't feel as if there is going to be sales beats. If anything, the beat could come on more margins and will be cautious throughout the year."
Some retailers, faced with plunging holiday-quarter earnings numbers, have declined to give any guidance at all for the current period.
Late Wednesday, department store chain J.C. Penney reported its same-store sales fell 32 percent during the fourth quarter as consumers failed to respond to the company's decreased emphasis on sales and promotions.
(Read more: JC Penney's 180 Is Complete)
Ron Johnson, J.C. Penney's chief executive, declined to divulge sales details for its current quarter, saying he wants to "stay out of the guidance business."
Some in the restaurant space are also feeling the pinch.
Darden Restaurants, which owns the casual dining chains Oliver Garden, LongHorn Steakhouse and Red Lobster, said blended same-store sales at its three eateries would be 4.5 percent lower during its fiscal third quarter.
Clarence Otis, Darden's chairman and chief executive, said that "while results midway through the third quarter were encouraging, there were difficult macro-economic headwinds during the last month of the quarter."
"Two of the most prominent were increased payroll taxes and rising gasoline prices, which together put meaningful pressure on the discretionary purchasing power of our guests," he added.
To ease this pressure, Olive Garden plans to offer smaller plates, cheaper items and lower-calorie meals — changes that Otis said it has made to be "responsive to the financial realities of our guests."
In a nod to consumers' search for value, fast food chain Burger King slashed the price of its Whopper Jr. sandwich to $1.29 from around $2 for a limited time while increasing its advertising on value-menu products.
Larry Miller, analyst at RBC Capital, told CNBC that there are many factors that are creating "some noise" right now in the restaurant space.
"Our view has been that the payroll tax would take a bigger bite out of industry traffic than people were realizing," Miller added. "If you look at the numbers, and you just assume there's an equal cutback from consumer spending as a reduction to the payroll tax you're losing about a point to a point and a half in industry traffic. So I think there's something there. There's certainly something to the delayed tax refunds, that's certainly hurting."
-By CNBC's Katie Little; Follow her @katie_little_
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