The claim is true.
According to BBC, the shutdown of the U.S. federal government lasted 43days because the Congress failed to approve a new funding bill. Although both chambers of Congress must approve a spending plan to send to the president to be signed into law, it took longer than expected because it was difficult to agree with the bill. Also, during the shutdown, many public services, including airports, were disrupted.
In addition, CBS also reported that this was the longest government shutdown in the U.S. history.
Therefore, I believe that the claim is true from these reliable resources.