Failed attempts by the national government to ameliorate economic problems of monopolies and child labor in the late nineteenth and early twentieth centuries were a result of

One possible explanation for this failure is the strong intersection of politics and private interests during this time, similar to what exists today. Super-wealthy capitalists, made rich by the Industrial Revolution, enjoyed great power in all areas of public life, due to their tremendous portion of the nation's total wealth. This enabled them to influence politics and prevent reforms that would crack down on trusts and child labor. 

The Industrial Revolution itself, namely its sudden transformative effect on the country, also contributed to these issues. The return (profit) on capital became huge compared to the return on labor (wages), so that the owners of this capital became too powerful for healthy competition to exist, creating monopolies. This meant they could afford to dictate the wage rate on unskilled labor, since they were offering most of the jobs available.
Society had to transition from an agrarian economy in which families owned farms, often working the land with their families and selling their products themselves (acting as both the capitalist and the laborer), to an industrial economy, in which a huge corporations dictated the work hours, wages, and conditions. Children who once contributed to the household by working at their parents' discretion now worked long hours for companies in squalid conditions, where their interests and rights were protected and valued by no one.

A third reason, in the specific case of the United States, is that federal laws governing the free market were controversial among many Americans, not only the rich, because they seems to infringe on many of the founding principles of the country. Federal overreach has always been a sensitive issue in the country, and laws governing the organization of companies and a child's "right to work" were interpreted by many as Uncle Sam overstepping his boundaries.