The ad, which would have run on the TNR homepage, read, "Is Your Vote For Sale? Sean Eldridge Thinks So..."
Bob Brennan, sales director at TNR, originally considered running the ad, but declined to do so once he realized the ad criticized Hughes' husband, according to Politico.
Brennan reportedly wrote to the NRCC Monday to inform them of his decision.
"We reserve the right to approve all creative which runs on our site," he wrote. "Your creative does not meet with our approval. Thank you for considering The New Republic."
The website told Politico that the decision is in line with its ad policy.
"The New Republic has always reserved the discretion to choose which companies and organizations we partner with for our advertising," TNR spokesperson Annie Augustine told Politico Monday.