[edit1] The closet thing I can find is that senate republicans aren't co-signing bills to add more regulation. Not that they're trying to grant immunity to Equifax. http://www.pbs.org/newshour/rundown/equifax-breach-congress-...
[edit2] And at the end of the article:
> Even if the Equifax breach fails to bring about the passage of new legislation, it has scuttled one bill in the works. On the day of Equifax’s announcement, a House subcommittee examined legislation that would have decreased the potential consequences when consumer reporting agencies falsely malign someone. Such mistakes can haunt consumers for years.
> The bill would have eliminated punitive damages for violations of the Fair Credit Reporting Act. The bill’s sponsor, Rep Barry Loudermilk, R-Ga., said the legislation was aimed at curbing frivolous lawsuits and would not have granted any immunity to Equifax for the data breach. “Nevertheless, given the unfounded attacks on me and the rampant misinformation circulating about this legislation, the Financial Services Committee has not scheduled further action on any bill at this time.”
So I suppose there was bill that could have done that, but it's dead now.