Trades argue measure will allow consumers and financial institutions to sue over damages from card data breaches.
Members surveyed also reported their average Target breach cost was $45,000.
In advance of Monday's Senate Banking Committee hearing on data security, bank and credit union trades urge action on issue.
Georgia Democrat Hank Johnson said he would support an "oversight investigatory hearing to probe into that matter."
Bipartisan legislation would require entities, including financial institutions, retailers and federal agencies, to investigate breaches and inform consumers.
Data security bill, sponsored by Sen. Patrick Leahy (D-Vt.), includes criminal penalties for those who conceal a breach.
Although some of the names are still unofficial, party choices for Senate committees that affect credit unions are starting to emerge.
Credit unions and other opponents of the Federal Reserve’s proposed rule capping debit interchange fees received good news last week when bills to delay the rule’s implementation were introduced in the Senate and House.