Yes, it could.

When you log into an online government service, a secure (HTTPS) connection is established. This means that the data transferred between your browser and the government's authentication server is encrypted so that no one can intercept this communication. When a virus scanner scans such a connection, and thus places itself between the two parties, the security protocol protecting that connection will consider the scanner as 'criminal' activity. The authentication process is then aborted.

With most virus scanners you do have the option of not scanning certain URLs, such as those of online government services. To ensure that you do not make your computer unnecessarily vulnerable to viruses, consult the distributor of your antivirus software. They can help you adjust the configuration of your virus scanner so you will still be safe yet no longer experience this problem.