(CNN) While President Donald Trump's incendiary tweets and unorthodox behavior dominates headlines, well-heeled conservative groups and lobbyists are trying to focus their energy elsewhere, spending significant resources to push through what could be the most important legislative goal of Trump's first year: Tax reform.

The network of conservative groups assembled by billionaire donors Charles and David Koch are executing a major initiative to pressure lawmakers to overhaul the tax code, a goal that has eluded congressional leaders for decades. The Koch-backed groups did not openly support Trump's candidacy for president -- Charles Koch said last year that the choice between Trump and Hillary Clinton was like choosing between cancer and a heart attack. But now that a Republican is in the White House, the Koch's sprawling network is aiming to take advantage of the GOP's grip on Washington.

But the challenges to accomplishing a tax overhaul are many.

"It is a Herculean lift," said Tim Phillips, president of the conservative advocacy group Americans for Prosperity.

Furious after the Republican-held Congress failed to repeal former President Barack Obama's signature health care law, leaders of the Koch-backed groups mince no words when discussing how Republican voters and groups would respond if GOP leaders fall short of passing a tax overhaul bill as well.

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