According to the dictionary meaning, a 'Vaishnava' is necessarily a 'Worshipper of Vishnu'.
वैष्णव a. (-वी f.) [विष्णुर्देवतास्य तस्येदं वा अण्] 1 Relating to Viṣṇu; गां गतस्य तव धाम वैष्णवम् R.11.85. -2 Worshipping Viṣṇu. -वः 1 One of the three important modern Hindu sects, the other two being Śaiva and Śākta sects
I have found some people brand Sri Vishnu' as a 'Demi-God' while calling themselves 'Vaishnavas'! Reference : http://www.krishna.com/info/demigods
What is the position of Lord Vishnu in the different 'Vaishnava' sects?