Amid great secrecy, about 200 of America's wealthiest and most powerful individuals from the worlds of finance, big business and rightwing politics are expected to come together on Sunday in the sun-drenched California desert near Palm Springs for what has been billed as a gathering of the billionaires. They will have the chance to enjoy the Rancho Mirage resort's many pools, spa treatments and tennis courts, as well as walk in its 240 acres away from the prying eyes of TV cameras.

But the organisers have made clear that the two-day event is not just "fun in the sun". This will be a meeting of "doers", men and women willing to fight the Obama administration and its perceived attack on US free enterprise and unfettered wealth.

As the invitation says: "Our goal must be to beat back the unrelenting attacks and hold elected leaders accountable."

The reference to the accountability of America's elected leaders is ironic, bearing in mind that the gathering has been convened by two brothers who have never been elected to public office and are among the most unaccountable and secretive political players in the country.

David and Charles Koch enjoy a combined fortune of $35bn (£22bn), run the second largest private company in the US, Koch Industries, and are increasingly using their fabulous riches to push their special interests within America's political process. Nobody knows precisely how much they spend on influencing elections and lobbying Congress, but it is thought to be scores of millions of dollars.

By similar vein, the guestlist for their gathering on Sunday is unknown. Past attendees at the twice-yearly event include supreme court judges, rightwing media celebrities such as Glenn Beck and Rush Limbaugh, prominent governors of southern states such as Bobby Jindal (Louisiana) and Haley Barbour (Mississippi), as well as leading figures from Wall Street and energy companies, and titans of industry.

The format of the gathering will be similar to previous Koch events, the last of which was held in Aspen, Colorado, in June. The assembled tycoons will talk about some of the Koch brothers' pet horrors – the growth of government and state regulations, what they call climate change "alarmism" and "socialised" healthcare.

Then they will share ideas about how to tighten their grip on politics and the judiciary by shaping election campaigns.

But this year's reception will differ in one important regard: it will have an opposition. For the first time, a coalition of progressive and liberal groups has formed to try to counter the power of the Koch brothers.

The anti-Koch gathering will be staged down the road from the Rancho Mirage. It will hold its own – open, as opposed to secretive – panel discussion and a rally designed to highlight what its organisers see as the pernicious impact of the Kochs on the democratic process.

"We want to raise public awareness of the harmful influence of corporate money. The Koch gathering embodies all that we consider damaging to our democracy," said Mary Boyle, of Common Cause, a campaign group that has spearheaded the opposition.

Among the panel speakers will be Robert Reich, the labour secretary under Bill Clinton. He believes the Kochs represent what he calls a perfect storm that is battering American democracy. "This is the worst I've seen it in my lifetime. In the late 19th century, robber barons would deposit bags of silver and gold on the desks of legislators. We've progressed significantly since then, but once again big business is engaging in politics."

The reach of corporate agitators personified by the Kochs has been greatly extended by Citizens United, a landmark ruling by the supreme court in January 2010 that opened the door to corporate spending on political campaigns for the first time since 1947. The ruling led to a splurge of secret outside funding in the 2010 midterm elections in which about $300m was spent, a threefold increase on 2006.

The Koch brothers made good use of the ruling. Again, how much they invested in the elections is not known, but Americans for Prosperity, the Tea Party-aligned movement founded and funded by the Kochs, has put its own spending at $45m.

Common Cause this week called on the US attorney general to investigate a possible conflict of interest. The group pointed out that two supreme court judges – Clarence Thomas and Antonin Scalia – had taken part in strategy sessions in a previous Koch gathering. Both ruled in favour of lifting the ban on corporate political spending, a move that directly forwarded the Koch brothers' political aspirations.

"What we are seeing is a form of legalised bribery," said Rick Jacobs, founder of the Courage Campaign that is participating in Sunday's counter-gathering. "Here are the Koch brothers with their unbridled wealth, using it to shape society as they see fit. It's our obligation to do everything we can to stop them."

Critics of the brothers point out that many of the ways they seek to influence politics serves their own personal and corporate interests. They lobby for lower personal and corporate taxes, which doubly benefits them as individual taxpayers and as owners of a company with an annual turnover of about $100bn.

Since 2006, the Kochs have been the largest political funders of any energy company in the US. They have backed thinktanks and campaigns that have spread doubts about climate change, which suits their purposes as oil and coal magnates who have been named among the top 10 air polluters in the country.

Their sustained fight through the Tea Party movements against government regulations also benefits their multiple concerns, that range from oil pipelines to paper cups, wood, carpets and Lycra.

"I don't want to demonise the Koch brothers personally," Reich said. "But they demonstrate how vast wealth is now being funnelled into the political process in secret, undermining our democracy."

Attendees of past Koch gatherings

Justice Clarence Thomas: A member of the US supreme court since 1991, he tends to vote with the majority conservative wing of America's highest judicial panel. His wife, Virginia Thomas, is a lawyer active in rightwing politics, having founded and led until the end of last year Liberty Central, a group that opposes what it sees as the "tyranny" of the Obama administration.

Glenn Beck: The notorious Fox News commentator is also a hugely successful businessman, earning $32m last year from his empire of TV and radio shows and books. This week he was the subject of an open letter from 400 rabbis who protested against his persistent references to Nazis and the Holocaust as terms of abuse against leftwing opponents.

Senator Jim DeMint: The senator for South Carolina is one of the most consistently rightwing members of the Senate and a darling of the Tea Party movement. David Koch has personally singled out DeMint for praise after the politician vowed to destroy Obama's healthcare reforms.

Fred Malek: A former aide to George Bush, Malek was one of the top fundraisers for the $56m attack ad campaign that senior Bush adviser Karl Rove unleashed in the 2010 midterm elections, directed against Democratic candidates.

Steve and Betty Bechtel: Some of the many industrialists who have attended past Koch events, they own the largest engineering company in the US, the Bechtel Group.

David Chavern: No 2 at the US Chamber of Commerce, a business coalition that spent up to $75m on launching attack ads largely against Democrats in the 2010 midterm elections – twice the amount it spent on the 2008 elections.