When President Obama treks to Los Angeles — again — on Feb. 15, he’ll be looking to convey the sense of a winner: Improved poll numbers and a brightening economy, as well as the bandwagon effect of a smattering of stars coming out in support. The Foo Fighters will be playing for him, and Will Ferrell is among the co-hosts of a high-dollar event at a posh Beverly Hills estate.

But even as the campaign tries to reignite enthusiasm of the last election cycle, there remains some dismay among the highest echelons of studio and media executives over the way the White House responded in mid-January to a pair of anti-piracy bills in Congress, stopped in their tracks after the administration criticized parts of the legislation amid an Internet-fueled e-mail storm of protest that flooded Capitol Hill to oppose the measures.

In the immediate aftermath, MPAA chairman Chris Dodd and some studio chiefs suggested that the industry wouldn’t be as willing to step up to the plate and serve as a favorite campaign ATM if politicians weren’t onboard to back Hollywood anti-piracy initiatives. In the days after the Internet blackout, Fox’s Jim Gianopulos said, “I have been a very early and ardent supporter of the president, but I couldn’t say at this time that I am very enthusiastic about providing support. If you went to Detroit and said, ‘I think the Japanese build better cars,’ I don’t think you would feel a wellspring of support if, as a candidate for office, you went there for fund-raisers the next week.”

As headline-making and attention grabbing as the Stop Online Piracy Act fracas was, what it has yet to do, and is unlikely to do, is realign the way that Hollywood has traditionally stepped up to the plate in the political process: There are the motivations at the corporate level, and there are those of the broader creative community. The former is generally more mindful of the industry’s self-interest; the latter has a host of concerns and causes on which they will choose one candidate or the other.

This is not to say that studio anger isn’t real: One Obama fundraiser said that became clear when he sent out queries to some in the upper studio ranks, and the response was an immediate no.

What particularly irked studio chiefs was that the administration appeared to buy in to the idea that the legislation as written would pose a threat to free speech, a prospect that the Hollywood lobbies have long argued is a fiction advanced by the Googles of the world to stir up grassroots opposition.

But in the days that followed the SOPA lather, high-ranking studio execs were especially irritated when Obama’s reelection campaign sent out an e-mail trumpeting the White House’s position, noting that the administration had taken a stand that they “will not support legislation that reduces freedom of expression or undermines the dynamic, innovative global Internet.” “Folks spoke out on this issue — and President Obama listened,” James Kvaal, national policy director for the campaign, wrote to supporters. Included was a link to a campaign petition gathering names to “stand with the president for a free and open Internet.”

One high-level media executive who did not want to be named said that it was like salt in the wound, something that will not be easily glossed over in the months ahead.

But in the days that followed, it became immediately clear that if moguls were going to abandon Obama, they were going to be sitting it out rather than switching over to a Republican candidate friendlier to their concerns. All the 2012 contenders from the right came out against SOPA. (It also will take GOP front-runner Mitt Romney quite a while to catch up as concerns showbiz donations: According to the Center for Responsive Politics, Obama has raised $1.2 million from biz sources to Romney’s $152,900.)

Other influential figures, like Jeffrey Katzenberg, quickly made it clear that they were not backing away from Obama’s campaign. And few if any star names, the ones who can really draw attention from the broader public, were willing to publicly express their dismay at either the White House or the way that the whole debate played out. On Jan. 18, the day of the Internet blackout, Obama was rasing money at the home of Spike Lee. As was noted at the event, Lee has been a critic of the president, but it hasn’t been over SOPA.

On Jan. 31 and Feb. 1, Michelle Obama headlined two fundraisers in Los Angeles, with no sign that support had waned. A lunchtime fundraiser went well beyond projections, Ken Solomon, CEO of the Tennis Channel and the campaign’s Southern California finance, said last week. The events this week, at the Beverly Hills home of Colleen and Bradley Bell, were selling at a “record pace. We are selling out, and it is early to almost be sold out.”

Solomon added that over the long term, what is becoming obvious is that the issue is far more complex than the White House choosing between Hollywood and Silicon Valley, as the administration made it clear something had to be done in Congress about piracy.

Last week, Barbra Streisand posted a statement bemoaning Republican rivals’ rhetoric and praising Obama’s progress on the economy. “Because of the President’s policies, our economy is on the road to recovery, and it’s time we start celebrating the truth,” she wrote. There was no mention of piracy or SOPA.

Hollywood undoubtedly leans left. But it doesn’t march in lockstep, particularly when it comes to its own issues.

Among many politically engaged creatives, the failure of SOPA, seen as the industry’s biggest policy initiative in recent years, isn’t necessarily being blamed on the Obama administration, but rather that the industry’s PR effort to pass the bill was no match to the social media-led effort of opponents, and that some of the legislation’s provisions may have been an overreach. “There’s enough blame to go around,” said one industry topper. “We dropped the ball.”

More disconcerting for the Obama campaign is perhaps the extent to which pro-Obama SuperPACs are being outgunned by those of his potential Republican rivals. Last week, the campaign gave its endorsement to the most prominent of these, Priorities USA, run by two former White House aides. The hope is that it will be enough of a boost to engage Obama’s many bundlers to step up and give, in unlimited amounts.

As much as Obama will be courting supporters for four- and five- figure sums next week, his endorsement of SuperPACs stands to change the dynamic of Hollywood giving altogether. There’s the corporate and creative classes, and there are the megadonors, who are being tapped to write six- and seven-figure checks. A good sign is the willingness of Haim Saban, one of the most prolific Democratic donors, who said last week that he will “surely participate” in giving to SuperPACs, but he hasn’t decided which one. In the last cycle, he was a diehard supporter of Hillary Clinton, yet lukewarm to Obama in the general election.

Also working in the President’s favor is that the general election is not next week or next month. The policymakers in Washington now talk of letting emotions cool, letting larger sensibilities surface, and then making sure an anti-piracy deal gets done.

In other words, time heals.