(CBS News) — For years, Costco (COST) has been the retailer that could do no wrong. Until it messed with its customers’ credit cards, that is.

The retailer flipped to a new credit card on Monday, switching out its 16-year relationship with American Express to a new policy of only accepting Visa cards. As part of the deal, Costco switched its store-branded credit card to a Visa card from Citibank (C). The idea was to allow customers with Visa cards to use them at Costco, since they are more widely held than American Express cards. Analysts also expected the transition to lower Costco’s expenses, given that Amex charges retailers a higher fee than Visa.

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While in theory the switch was designed to be customer-friendly, this week has proved to be a headache for many Costco customers, who have taken to Twitter and the retailer’s Facebook page to vent their frustration over missing cards, double billing, and long wait times to reach customer service. Its Facebook page is headed by a graphic that shows the words “Costco + Visa =” followed by a red heart, at which one shopper took a potshot.

“Costco + Visa = Disaster,” the customer wrote. “You should have kept accepting Amex. At least the superior service matched your brand.”

Citigroup and Costco didn’t immediately respond to requests for comment.

Other customers complained that they had either received several new Costco Visa cards, or hadn’t received their replacement yet. Some cards weren’t linked to Costco accounts, while others had misspelled names or other errors. A few complained about double billing on both the Amex and new Visa cards. Many said their efforts to talk with Citibank customer service proved fruitless, undermining their confidence in the retailer.

“This is Costco’s issue,” another customer wrote. “They failed to manage their vendor, Citi. We never received our card and tried to mange this a week ago and Citi told us to wait. Citi could have mitigated issues by addressing problems early. Costco management should have been there making sure this occurred!”

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Given warehouse stores are in a competitive retail environment, Costco’s strong brand with customers had provided it with an edge over rivals such as Sam’s Club. Costco ranks at the top of the list of specialty retailers in the American Customer Satisfaction Index, which ranks companies and industries based on how consumers feel about their products and services. Costco’s ASCI score of 81, for instance, was far ahead of rivals Sam’s and BJ’s Wholesale Club, which both earned a score of 76.

The fiasco appears to be damaging some of Costco’s carefully cultivated goodwill, however. Some members vowed to shop elsewhere, or to cancel their accounts. Aside from the new Costco Anywhere Visa Card and other Visa cards, the company accepts cash, debit cards, checks, EBT and Costco cash cards.

Costco told customers on its Facebook page that they may face delays when calling Citi’s help line. It asked other members to write to costcocare@costco.com for help.

“Due to high levels of interest in the Costco Anywhere Card and high volumes of calls from cardholders, callers to Citi should expect longer than desired hold times. Citi is reviewing processes and pulling in additional resources to alleviate hold times,” Costco said on its Facebook page.

That response apparently isn’t enough for some customers, who are vowing to cancel their accounts or shop elsewhere.

“Did not expect a fiasco like this from Costco,” another customer complained. “We have not received the new Visa cards and wasted (a) couple of hours trying to talk to Citi personnel. Citi personnel could not even link my name to my Costco account number and hence cannot give me a card. That being the case, it looks like Costco is giving me no option but to cancel our account.”

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