“AT&T Inc. T +0.05% faces the possibility of a walkout by 40,000 wireline employees Sunday morning if the union can’t reach an agreement with the telecommunications giant on a new contract.

Members of the Communications Workers of America voted over the weekend to authorize CWA President Larry Cohen to call a strike after the contract expires on April 7. CWA members staged a two-week strike against Verizon Communications Inc. in August and have yet to reach an accord with that company.

AT&T is seeking increases in workers’ health-care premiums and co-payments, pension cuts and other benefits changes, according to the union.

“Everything leads me to believe that we’re in the same position today with AT&T that we were with Verizon last year,” said Chuck Simpson, president of CWA Local 2204 in Salem, Va. “Like so many companies, they want to shift more costs to the employees.”

On its website, AT&T said employees’ medical costs rose 54% from 2004 to 2010 and 8% in 2010 alone. “AT&T seeks to reach fair agreements with our union partners that enable a competitive cost structure reflecting current market realities,” the company said on the site…”

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