Back in the fall and before the election, Trump was talking about implementing a spending cutting plan called the "Penny Plan". If implemented, it would, year after year, cut one penny out the budget for every dollar of spending. An analysis by the Washington Post showed that after a decade of applying this technique, spending would be reduced by 23%. And, it could either be applied across the board or targeted to specific areas such as the EPA. The cuts would be gradual and not immediately earth-shattering.
However, after Trump took office, his budget cuts started to appear earth-shattering by aggressively targeting programs that political conservatives have never really like. It would immediately cut the EPA by 31%. The Department of Health and Human Services by 16.2%. He also would eliminate all spending for things like Public Broadcasting and the National Endowment of the Arts. It is these program eliminations that have the political left, and some on the right, in an uproar.
Trump is not going to get all the cuts he wants, and, quite frankly, I don't think most Americans will agree with the major changes and program eliminations he has proposed. The final budget has to be approved by May 15th, and I strongly suspect that the Republican controlled Congress will cave and only moderate reductions will be made. They want to keep their jobs after the 2018 election. Congress is always good at creating spending, but never really willing to make cuts because of political consequences.
This chart shows how Trump’s ‘penny plan’ would add up to huge budget cuts: https://www.washingtonpost.com/news/wonk/wp/2016/09/16/this-chart-shows-how-trumps-penny-plan-would-add-up-to-huge-budget-cuts/?utm_term=.511c1525d4c5
CNN: Trump's budget would cut off funding entirely for several agencies, including arts, public broadcasting and development groups, and also proposes steep cuts to agencies like the State Department and Environmental Protection Agency: http://www.cnn.com/2017/03/16/politics/trump-budget-cuts/