As BP ramps up its public relations effort to stem the fallout of the oil spill crisis that has badly stained its reputation, the company faces another big hurdle this week when its gaffe-prone chief executive, Tony Hayward, testifies before a House panel.

Although other BP executives have gone before Congressional committees, this will be Hayward’s first Capitol Hill appearance. The London-based CEO has been the target of intense criticism for his handling of the crisis and for what have been viewed as insensitive remarks, including when he told reporters, “I’d like my life back.”

Hayward’s performance before the House Energy and Commerce Subcommittee on Oversight and Investigations on Thursday could be critical for his future at the company.

“I think this is do-or-die for him,” said Eric Bovim, CEO of Gibraltar Associates, a public relations firm.

Bovim was critical of BP’s public relations campaign, saying it was too reliant on traditional newspaper spots, which he said would have been more appropriate for the Exxon Valdez spill back in 1989 before the Internet age.

But BP has sought to polish its image in recent weeks, hiring a bipartisan media shop, Purple Strategies, which has produced a television spot featuring Hayward.

Purple Strategies is headed by Republican media strategist Alex Castellanos, who has advised a number of GOP presidential campaigns, including that of Mitt Romney in 2008, and Democratic consultant Steve McMahon, who was a senior adviser to Howard Dean’s 2004 presidential bid.

A consultant familiar with the BP deal said Purple Strategies was given the contract by Hilary Rosen, the D.C. managing partner of the Brunswick Group, a London-based PR firm, which has been handling much of BP’s media work.

The consultant, who spoke on condition of anonymity, said the ad contract is particularly tricky for Castellanos, whose clients have included Louisiana’s Republican Gov. Bobby Jindal, a critic of how BP and the federal government have handled the spill.

“The tightrope they are walking is amazingly dangerous,” said the consultant.

A woman who answered the phone at Purple Strategies said that the shop was not taking any questions on the ads and referred all calls to BP.

Neither BP nor Brunswick responded to questions about the public relations effort.

The Brunswick Group has also farmed work out to other politically connected consultants such as John Feehery, a former spokesman to then-Speaker Dennis Hastert (R-Ill.), who now heads the Feehery Group, which specializes in communication and government affairs strategy.

Feehery said his role is to provide rapid response to reporters on the spill.

“I just try to get the facts out,” said Feehery, who, for example, last week e-mailed the latest update on the number of claims that BP had paid out.

BP has also beefed up its in-house media team by hiring Anne Womack-Kolton, former press secretary to Vice President Dick Cheney, to head the company’s U.S. media relations.

And BP has sought more control of its message on the Internet by paying to make BP’s website among the first links that pop up when people search for oil spill.

Getting on Message

The beleaguered oil giant is getting some assistance from others in the industry who had largely remained in the background. The American Petroleum Institute, the trade organization for Big Oil, last week launched an ad campaign with print and radio spots to highlight that it is helping BP deal with the spill.

The expanded media campaign has generated criticism from some Members of Congress who believe the company should be devoting its resources to plugging the leak and cleaning up the spill.

Last week, several Democratic Members — including Reps. Peter Welch (Vt.), Lois Capps (Calif.), Paul Tonko (N.Y.) and Steve Cohen (Tenn.) — held a news conference blasting BP and asking the company to suspend its PR efforts until the oil is cleaned up.

One energy expert said Hayward faces a no-win situation appearing before lawmakers who are intent on drawing blood.

“It is not a hearing for substance. It is a hearing for show,” said Frank Maisano, a crisis communication and energy expert at Bracewell & Giuliani. “They want to make it clear they are getting tough on BP.”

Maisano said that the pugnacious Energy and Commerce Chairman Henry Waxman (D-Calif.) will be a formidable inquisitor.

“I fully expect Waxman to be on top of his game,” he said. As for Hayward, Maisano said, “he has to survive and not put his foot in his mouth as he has several times.”

In a letter requesting Hayward’s presence, Waxman and Subcommittee on Oversight and Investigations Chairman Bart Stupak (D-Mich.) instructed Hayward to bring along other BP officials who are prepared to answer technical questions from lawmakers under oath. BP executives are also expected to meet with President Barack Obama later this week.

Transocean Turns to K Street

Others involved in the spill are also increasing their profile. Transocean, the owner of the Deepwater Horizon rig used by BP, tapped the services of the Capitol Hill Consulting Group less than three weeks after the April 20 explosion in the Gulf of Mexico.

According to a May 10 lobbying registration filed with Congress, the Capitol Hill Consulting Group lobbyists working on the Transocean account include the firm’s chairman, former Rep. Bill Brewster (D-Okla.), who formed the Congressional oil and gas forum in 1994 and was co-founder of the Blue Dog Coalition. Also on the team is Jack Victory, who had been senior adviser on energy and other issues for former House Majority Leader Tom DeLay (R-Texas).

To help with the media, Transocean has enlisted Brian Kennedy, a former press secretary to House Minority Leader John Boehner (R-Ohio) and ex-Rep. Richard Pombo (R-Calif.), then-chairman of the Resources Committee. Kennedy, who now works for FD Public Affairs, did not return a phone call.

Transocean officials also did not respond to inquiries about their public relations and lobbying efforts.

Green Groups Weigh In

Environmental groups, who are highly critical of the spill’s impact on the ocean’s ecosystem, have also increased their public relations efforts.

The Sierra Club and the League of Conservation Voters highlighted the pollution caused by the spill in print ads last week urging lawmakers to oppose a resolution that would have prevented the Environmental Protection Agency from curbing greenhouse gases. The measure, sponsored by Sen. Lisa Murkowski (R-Alaska), failed to pass.

The National Resources Defense Council has put up a video on its website that juxtaposes scenes of the damage caused by the spill with some of the comments by Hayward such as when he said the environmental damage from the spill is likely to be “very, very modest.”