This should do it:
EXEC sp_configure 'user connections', 0;
That will set the number of connections back to the default, which is 32767.
Once you have SSMS open, disconnect from the server in the "Object Explorer" Window. Then you should be able to create a new query window and connect to it there. Alternately, you could use sqlcmd.exe to connect from the command-line without having SSMS open, then run the command from there.
The setting is stored in the master database, and can be seen through the following statement:
FROM sys.configurations c
WHERE c.name = 'user connections';
sys.configurations is actually a view, defined as:
CREATE VIEW sys.configurations AS
WHERE is_not_use = 0
The only way to see the
sys.configurations$ table is through the Dedicated Admin Connection, more commonly known as the DAC. The DAC needs to be turned on through SQL Server Configuration Manager, since it is off by default in SQL Server Express.