Actually, the Federal government did not have the power to stop child labor unless that labor was involved in interstate commerce. Actions to stop child labor could only be stopped by the states. The abuses of child labor came to the forefront during the progressive era; and many efforts at that time were made to stop it; but this was done by state action, not by the federal government. The National Child Labor Committee succeeded in having Congress pass an Act prohibiting child labor in 1902, but the bill was struck down by the Supreme Court as unconstiututional. The problem was the language of the tenth amendment, which states:

The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.

The Constitution did not give Congress the power to regulate labor, therefore the Supreme Court struck down the statute. Attempts to secure a Constitutional amendment were not successful. In 1948, Congress passed the Fair Labor Standards Act which limited child labor for any work which involved goods passing through interstate commerce.  At that time, however, many states on their own volition had passed laws strictly limiting child labor.

There are at least two reasons for this.

First, the US government at that time was very dedicated to the idea of laissez-faire.  The government believed that it was wrong to interfere in the relationship between workers and employers.

Second, the US was not yet a rich country and its industry was just expanding.  In that sort of an environment, child labor is often necessary.  Families need children to work in order to help support the family.  Industry needs child labor to help keep costs down so their products will still be affordable.

For these reasons, it would have been very difficult to ban child labor in the US in, for example, the late 1800s.