In the absence of federal labor laws, the general landscape of labor relations between employees and employers would like look like it did in the late 18th and early 19th centuries. During this time, employees had very little rights in the workplace. As a result, labor conditions were poor, with many workers working in dangerous or unhealthy environments with little safety procedures or protocols in place to protect their health. Equipment was not monitored for safe operating conditions, and hazardous chemicals were not contained or handled properly. Also, workers had very little personal rights and were subject to the whims of their employers in terms of wages. Also, there were no such things as benefits (vacation and sick pay, retirement plans. etc.).
This all started to change in 1935 with the passing of the National Labor Relations Act (also called the Wagner Act). This law gave workers to right to unionize and collectively bargain for better wages, rights, and working conditions. Before this law, if workers attempted to unite together to effect change, businesses could use legal means to punish or penalize them. The NLRA lead to the formation of unions and the unionization movement in the US. Unionized workers were able to negotiate for better working conditions which eventually lead to the creation of things like OSHA (Occupational Health and Safety Administration), a federal agency that outlines rules and regulations for all workers in the US, both unionized and non-unionized. In addition, the unionization movement also lead to the establishment of basic workers benefits like paid vacation and rules for sick leave so a person would not lose their job in the case of a bad illness. It should be noted that federal labor law also protects workers who choose not to join a union from being persecuted by unionized labor organizations.
If federal labor laws did not exist in the US today, working conditions would likely deteriorate to be more like they were in decades past. The competition of US and European labor with businesses in developing nations where no labor laws exist is fierce. Businesses in parts of Asia and Central and South America do not have the expenses that come with organized labor and as such are able to operate with a much lower labor margin, thus attracting more businesses to locate or outsource there. If the US had no federal laws regulating labor, working conditions in this country would like fall to those of developing nations in order for businesses to maximize profit with cheaper labor.