The NRCC released the statement Wednesday afternoon. By about 8 p.m. on Tuesday the race had been called for Brat. Here is the NRCC's statement from NRCC Chairman Rep. Greg Walden (R-OR):
Eric Cantor has been a steadfast leader for our party, and a great friend and mentor for so many House Republicans. I know Eric will continue to lead on the issues he cares so deeply about. Virginia families have selected Republican David Brat to represent them in Congress. I congratulate him on his victory and look forward to working with him in Congress.
Walden has also been reportedly indicating that his committee plans to support Brat in the general election.
I just spoke to NRCC chair Greg walden. they will support Dave brat. "He's the nominee," he told me. He is confident they'll hold the seat
— Jake Sherman (@JakeSherman) June 11, 2014