The announcement marks a new chapter in the strained relationship between the Trump administration and the expanding conservative network created by billionaire industrialists Charles and David Koch, who refused to endorse the Republican president in 2016.
"A lot of the good that the president's policies have done for the country so far can be undone by trade wars and tariffs", Pope said in an interview Sunday evening.
Republican officials on Tuesday privately interpreted what the Kochs did as a warning shot, meant to convey that siding with Trump, while politically enticing, will carry a political cost with their groups.
It comes as the Kochs unveiled an ad buy to fight against Trump's tariffs.
The Koch brand - including the privately held energy company Koch Industries - has become synonymous in political parlance with pro-business policies and libertarian ideology.
The Washington Post reported that at a reception held by the Koch network over the weekend, officials revealed a new approach-distancing themselves from the GOP and becoming less focused on partisan politics.
Charles Koch (L) and David Koch are seen in this combination picture.
Calling their network "highly overrated", he added: "I have beaten them at every turn.
We look forward to working with anyone to do so", James Davis, a spokesperson for the Kochs' political network, told CNN in a statement. "But if you're a Democrat and you stand up to Elizabeth Warren and corral enough votes for financial reform. you're darn right we'll work with you".
The midterm strategy could change in the coming weeks, but the Kochs now plan to ignore North Dakota's high-profile Senate contest, where three-term Republican Congressman Kevin Cramer is trying to unseat Democratic Sen.
The Koch network is now only supporting for Republican candidates for Senate heading into midterm elections: the GOP candidates in Wisconsin, Tennessee, Missouri and Florida.
The Koch network is "raising the bar and raising expectations" of GOP lawmakers, and said Monday it will freeze its support of anyone who breaks with its views because some Republicans are taking its support for granted, The Hill reports.
But once Trump took office, he appeared to have made peace with the Koch network. "They love my Tax & Regulation Cuts, Judicial picks & more", Trump tweeted.