Obama drew fierce criticism when he appointed Block and Griffin, among others, in January 2011.
At the time, the Senate was holding pro forma sessions to prevent the president from acting. The Obama administration has argued the Senate was actually in recess at the time.
Late last month, the U.S. Court of Appeals for the D.C. Circuit ruled the appointments were unconstitutional.
The administration is expected to appeal the ruling.
Kelly introduced his legislation last week, and had more than three-dozen co-sponsors on the bill by late Thursday. Similar legislation is pending in the Senate.
In the meantime, Obama this week asked the Senate to confirm Block and Griffin, prompting another flare-up within the GOP. Several House Republicans — including Speaker John Boehner (R-Ohio), Majority Leader Eric Cantor, (R-Va.), Majority Whip Kevin McCarthy (R-Calif.) and House Education and Workforce Committee Chairman John Kline (R-Minn.) — sent a letter to Obama Wednesday asking him to nominate “qualified individuals” to the board.
They also sent a second letter to NLRB Chairman Mark Pearce, asking him to cease the board’s work until the Supreme Court decides the matter.
Kelly’s bill has been referred to Kline’s committee for consideration.