WASHINGTON  The drug industry has authorized its lobbyists to spend as much as $150 million on television commercials supporting President Obama’s health care overhaul, beginning over the August Congressional recess, people briefed on the plans said Saturday.

The unusually large scale of the industry’s commitment to the cause helps explain some of a contentious back-and-forth playing out in recent days between the odd-couple allies over a deal that the White House struck with the industry in June to secure its support. The terms of the deal were not fully disclosed. Both sides had announced that the drug industry would contribute $80 billion over 10 years to the cost of the health care overhaul without spelling out the details.

With House Democrats moving to extract more than that just as the drug makers finalized their advertising plans, the industry lobbyists pressed the Obama administration for public reassurances that it had agreed to cap the industry’s additional costs at $80 billion. The White House, meanwhile, has struggled to mollify its most pivotal health industry ally without alienating Congressional Democrats who want to demand far more of the drug makers. White House officials could not immediately be reached for comment.

Many Democratic lawmakers have railed for years against what they consider the industry’s excessive profits and pointedly insisted in recent days that they do not feel bound by the White House’s commitments.