The pharmaceutical giant spent big bucks amid key international negotiations last year to protect record earnings.
As a consumer protection subcommittee chairman, Blumenthal has focused on the role pharmaceutical benefit managers play in driving up the cost of drugs.
Lobbying giant PhRMA reported revenues of more than $600 million in 2021, a new record for the group.
The dark-money group Center Forward, which is buying the ads, has received millions from the pharmaceutical industry in recent years.
Four Republicans with extensive ties to the pharmaceutical industry have already said they plan to cross the aisle and support Califf's confirmation to be commissioner of the Food and Drug Administration.