BP , under pressure from the White House and Congress, is now weighing a dividend cut. “We are considering all options on the dividend,” CEO  Tony Hayward told the Wall Street Journal Thursday. “But no decision has been made.”

The comments come as public outrage builds against the company’s handling of its Gulf Coast oil spill. Just a week ago, BP was saying it had the resources to pay for the cleanup and maintain its $10 billion-a-year dividend.

But as the scale of the Deepwater Horizon disaster becomes clear, Wall Street is starting to have its doubts. Among the biggest questions is the scope of the company’s legal exposure.

The cost of insuring against a default on BP’s debt has risen more than tenfold since the end of April, when the spill first started getting front page treatment, and a plunge earlier this week briefly left BP stock down $90 billion from its preblowout level.

But as bad as BP has looked throughout this fiasco, the problem isn’t its alone. Notably, Transocean — which owns the rig that blew up on April 20, killing 11 workers and injuring 17 — has seen its shares drop in lockstep with BP, and its credit default swap spreads soar, in spite of the company’s claims that it is protected against outsize legal costs by an indemnification agreement with BP.

Wall Street analysts have been urging investors to buy Transocean, arguing that it is undervalued based on even conservative earnings forecasts assuming Gulf drilling is pared back. One bull has been so sure of the Transocean-is-cheap case that he has had a buy on the stock since it traded at $120 — $75 above its recent price.

Bulls on the stock have mostly accepted the company’s claim that its deal with BP protects it legally.

But does it? Fortune’s Roger Parloff suggests the case isn’t airtight.

“Notwithstanding Transocean’s assertions, BP’s lawyers evidently have some theory under which they think they can invalidate the oil-spill indemnification agreements Transocean thinks it’s protected by,” he writes. “BP has already sent a demand letter to Transocean’s excess insurers, seeking to tap the $750 million in insurance obligations they owe to Transocean. ”

At the very least, the expanding political and legal profile of the case could put Transocean under some of the same pressure BP has felt. Some Congressmen last month called for an investigation of Transocean’s decision to start paying a $1 billion dividend next month, but little has been heard of the issue since.

Transocean notes that the dividend payout decision was made before the Deepwater Horizon disaster, and insists it will have the resources to pay its share of claims tied to the case. Because BP is a household name and Transocean a company few outside of Houston have even heard of, cracking down on Transocean — even if Congress had any power to do so — isn’t likely to become a national cause.

“Transocean will honor all of its legal obligations arising from the Deepwater Horizon accident,” the company said.

But this is hardly a warm and cuddly company. It moved to Switzerland two years ago to cut its taxes, after a run of tax disputes in this country. It infamously filed last month to limit its liability in the case to $27 million, after receiving hundreds of millions of dollars in insurance proceeds.

Clever, but the time for cleverness in this debacle has come to an end. It’s time for Transocean to heed common sense and call off its dividend.