I2 is a very fast and fat network. Because of it's throughput and network speed it will make gov't more effective and efficient due to faster delivery and gathering of information. Because of the better throughput, offices could take advantage of other advances in technology, such as voice/video over IP - replace traditional land lines with cheaper voice/video IP phones. Extremely large amounts of data could be transmitted or received and processed much quicker with an I2 connection.
As an example, my office has 2 T1 lines for a combined total of 3Mbits/sec. I2 currently provides nearly 9Gbits/sec ... and later this year will start averaging speeds of about 100Gbits/sec. My office needs to download very large gigabyte size files but cannot do so efficiently at the moment due to our network setup. We also generate equally large files that we'd like to make available. An I2 connection would make dissemination and acquisition of this data much more efficient.
A happy side effect of having gov't offices connected up to I2 is that the infrastructure would be laid so that neighboring communities could also begin to make their own connections to I2 (thus improving local economies and spurring on greater innovation and economic growth for the nation).