Why don't many people from Tamilnadu support Narendra Modi's Government?

There are two sides to the BJP - the Hindutva side and the capitalist side. Both have trouble penetrating TN due to ideological differences. There are 4 factors - language, religion, caste and economics.

Hindutva politics plays well in places with about 20% minority population. BJP could take Jammu because the Hindus there fear about the Muslim minority. In most parts of Tamil Nadu, it is 90%+ Hindu and in some parts it is all Hindu. You can see Hinduism everywhere - in offices, government symbols [only state with a Hindu temple as the official symbol], schools and colleges. Thus, Hindus in most of TN don't see a big threat of other religions and don't see the need to protect their religion. Selling Hindutva to Tamils is like selling ice to Eskimos.

The only two regions in Tamil Nadu with a higher concentration of minorities is in the extreme south - Nagerkoil and extreme northwest - Nilgiris. These are the only places BJP has historically won in TN.

Then there is the Brahmin factor. Since the 1960s, Dravidian parties have made Tamil society think national parties as Brahminical forces. First, it was the Rajaji-led Congress that was the tool of Brahmins and now the BJP. Given the strong anti-Brahmin wave since the 1960s, it is hard to get anyone elected with a Brahmin background and plenty of BJP leaders are Brahmins. Jayalalitha was the only Brahmin leader in present TN politics and she got through by being mentored by MG Ramachandran and through populist measures like drastically increasing caste quotas.

Now, coming to the capitalistic part. Tamil Nadu economics have been traditionally government driven. It is among the most socialist of Indian states. The trust for government has been traditionally higher than in other states. Government sector accounts for a big chunk of employment and government employees at lower rung tend to hate capitalism as their job is in line. The movies are filled with all sorts of rants against capitalism and I have never seen a good Tamil movie that actually praised the power of liberalization. While it is not as bad as the neighboring Kerala, but anti-capitalism is a very popular theme in many parts of TN.

The final element is language. BJP has traditionally pushed Hindi as the common language for India and this irks many Tamils. Tamils point to the idea that India is not an homogeneous entity and the thing that makes it special and unique is diversity. Whether you agree with that idea or not, it should be understood that anything that threatens the existence of Tamil is a very hard sell in Tamil Nadu. When a state's name starts with the language's name, you can realize how important language is to its existence and identity.

Some lessons for BJP:

1. Rediscover the idea of Hinduism: Tamils are used to listening to sophisticated Hindu philosophies from the likes of S. Radhakrishnan, Rajaji, Aurobindo, Bharathiyar etc. Even non-Hindus like Abdul Kalam had superior understanding of Hinduism. Crude versions of Hinduism from some BJP leaders doesn't sit well in TN.
2. Rediscover the idea of India: Some non-Tamils have this preposterous idea that Tamils resent to being in India, just because they oppose Hindi as a national language. If Tamils resent to India, Tamil Nadu would be having separatist movements. Rather its sons like AR Rahman are composing patriotic songs. Tamils like Subramanya Bharati had the vision for a unified India and I hope BJP leadership learns from that. Nationalism doesn't mean homogenisation. Instead of blindly copying other countries, BJP leaders should understand that India's uniqueness lies in having strong national bonds without a national language. Just as a swan doesn't need to imitate a duck, India doesn't need to drive everyone to a single language.