The President of the United States can just plain say "no". Talk about complete BS.
Not BS, its the law of the USA for 61 years.
"The Labor–Management Relations Act, informally the Taft–Hartley Act, is a United States federal law greatly restricting the activities and power of labor unions. The Act, still effective, was sponsored by Senator Robert Taft and Representative Fred A. Hartley, Jr. and legislated by over-riding U.S. President Harry S. Truman's veto on June 23, 1947; labor leaders called it the "slave-labor bill" while President Truman argued it would "conflict with important principles of our democratic society" despite subsequently using it twelve times during his presidency. The Taft-Hartley Act amended the National Labor Relations Act (NLRA; informally the Wagner Act), which Congress passed in 1935."
The law was passed over a presidental veto. That is, action by both the House and the Senate is required to override a presidential veto. A two-thirds majority vote of the Members present is required to override a presidential veto. If one house fails to override a veto, the other house does not attempt to override, even if the votes are present to succeed.
Clearly, the representives in Congress, at that time in an overwelming majority, decided to pass the law.
It is doubtful, that any president would invoke this law, as clearly it would be tough for the Boeing unions to hold the USA economy hostage, as could be the case in transportation issues. As our major airlines merge, and become more powerful, you may see this happen, as was done with the railroads much earlier.