You can specify the date as a constant string in the TestCase attribute and then specify the type as DateTime in the method signature.
NUnit will automatically do a DateTime.Parse() on the string passed in.
Example:
[TestCase("01/20/2012")]
[TestCase("2012-1-20")] // Same case as above in ISO 8601 format
public void TestDate(DateTime dt)
{
Assert.That(dt, Is.EqualTo(new DateTime(2012, 01, 20)));
}