The statement marks the first public criticism of the Trump administration from the Kochs, who oversee one of the most influential outside operations in conservative politics with a staff, budget and voter-turnout operation that rivals the Republican Party.
Charles Koch, 81, refused to support Trump's candidacy and had denounced the Republican's proposed ban on Muslims during the campaign as "reminiscent of Nazi Germany."
Koch did not refer to either Trump or his immigration order during public remarks Sunday afternoon to the more than 550 ultra-wealthy donors gathered at a luxury resort in the California desert for the network's annual winter summit.
During the meeting, however, Koch leaders stressed they were willing to work with the Trump administration and the Republican-controlled Congress. They also indicated they would throw their political might into opposing Republicans, if they bucked the network on key priorities, such as reducing government spending and regulations.
"We see big opportunities to work with the new administration and this new Congress," Hooks said. "It's this network's unique role to hold all politicians accountable, regardless of political party."
He warned of a dramatic swing back to the left in upcoming elections if Republicans lost sight of the economic worries that drove voters to Trump.
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Likely flash points with the GOP include $1 trillion infrastructure plan Trump pushed during the campaign and a possible plan to impose a 20% border tax on imports from Mexico that the network's leaders say will drive up costs for consumers.
"A $1 trillion government stimulus is a bad idea under Democrats and it's a bad idea for a Republican," Hooks said to loud applause from the audience that filled that ballroom of the Renaissance Indian Wells Resort and Spa.
Although network did not engage in the presidential race, its donors spent heavily to shape 2016 federal and state elections. All but one of their favored U.S. Senate candidates, Nevada's Joe Heck, won, helping the GOP retain control of the chamber.
Over the weekend, Koch officials said they intend to raise and spend $300 million to $400 million to influence policy and politics over the next two years.
That's a significant jump from the $250 million Koch groups plowed into politics during the 2016 election cycle and does not include the millions more donors that will send to other parts of the Koch operation to fund Charles Koch's philanthropic work, scholarships and grants to universities to advance his free-market ideas.
Donors, who pay $100,000 annually to the network, spent Sunday talking about policy fights, the election ahead and an array of programs the network backs — ranging from a project to help former inmates start businesses to the $26 million investment Koch's foundation and company have made to a non-profit that supports Historically Black Colleges and Universities.
In all, 11 elected officials were slated to make appearances at the three-day event. They included three governors, Wisconsin Gov. Scott Walker, Arizona Gov. Doug Ducey and Illinois Gov. Bruce Rauner and several U.S. senators. All are Republicans.