For years, issuers strove to make their credit cards "top of wallet" — the first one a consumer pulled out when making a purchase. Today, these lenders are jockeying for a different prize: whatever's left in the wallet.

Consumers "have a limited pot of money every month to pay bills," said Liz Jordan, a senior manager at the governance, regulatory and risk strategies practice of Deloitte & Touche.

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