GOP's Cantor welcomes union flip on Obamacare law

There's a "growing sense of commonality" among the White House, union leaders, and House Republicans that the president's health-care law is not ready for implementation, House Majority Leader Eric Cantor told CNBC on Thursday.

As rationale for that statement, Rep. Cantor, R-Va., cited three developments: The Obama administration's employer mandate delay earlier this month; a new letter from union leaders calling for changes in the law; and the 38th House vote to thwart Obamacare.

(Read more: House Republicans vote to delay Obamacare mandates)

Last week, the leaders of three major unions, including Teamsters head James P. Hoffa, sent a strongly worded letter to Democratic leaders demanding tweaks in the law to preserve the "well being of our members, along with millions of other hardworking Americans."

The letter also warned that, if unchanged, Obamacare would "destroy the foundation of the 40-hour work week that is the backbone of the American middle class."

(Read more: Obama boasts that health care law puts cash in 8.5 million pockets)

Cantor was sympathetic to those concerns, saying in a "Squawk Box" interview that part-time employment in this country is growing at the expense of full-time employment.

Because of the health-care law, the Virginia Republican argued, "employers are [also] beginning to rethink now whether they're going to be providing a benefit," which he added would break the president's "if you like your health care, you can keep it" promise.

—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC.