Final answer:
The statement in the question is false because when less than ten days remain in the congressional session, the president can perform a "pocket veto" by doing nothing, thus preventing the bill from becoming law.
Step-by-step explanation:
The statement that if fewer than 21 days are left in the congressional session and the president does not sign the bill before this period ends, the legislation becomes law by default is false. According to the legislative process outlined in the Constitution, when Congress passes legislation and forwards it to the President for signature, the President has several options.
The President can sign the bill into law, veto it, let it become law without a signature after ten days (excluding Sundays), or perform a "pocket veto" if Congress adjourns during the ten day period and prevents the bill's return. The pocket veto occurs during the last ten days of the congressional session when the President decides not to sign a bill into law, preventing it from becoming law by default due to the adjournment of Congress.