The government, as an entity, does not play a large role in the movie. However there are some instances where systems and policies put in place by the government influenced the actions of the main characters.
In the Context of the Film
The movie follows the team on Ben's first trip to Vegas and their endeavor through airport security. The team brought with them a large amount of cash which had to be smuggled through security. Ben, as the newcomer, had to stuff the cash down his pants and have the money go unnoticed through security. As the movie is set in the early 2000s Ben passed through a metal detector which was not triggered by the large amounts of cash he was carrying in his pants. However, more recently the Transportation Security Agency (TSA) has implemented more advanced imaging scanners which would have identified and likely flagged the cash that Ben was carrying in his pants.
Ben walking through the metal detector with about $250,000 in his pants
Image Credits: 21(2008)
The airport has become an important place when it comes to government surveillance and information gathering. Ever since the attacks on 9/11 airports have become some of the most surveilled and secured places in the country. Laws that were passed after these attacks loosened many of the privacy restrictions that encumbered government agencies in gathering information on individuals. Now, with the common enemy of terrorism people were more accepting to increasingly invasive and obstructive security and surveillance measures.
The only other significant connection the film has to the government is through the casino's database of biometric profiles of clients and security footage, which they can share with local and federal police if subpoenaed for the use of solving a crime.
It is also worth noting that card counting is not illegal, which is why when caught, the MIT team was dealt with internally as opposed to with the authorities/government, who likely would have additionally punished them for possessing fake identification cards.