The US, under Nixon, supported Pakistan in their invasion and genocide of East Pakistan (Bangladesh) and the subsequent Bangladesh Liberation War against India. The US has been historically allied with Pakistan. This may seem unintuitive at first, but there are many reasons for this, ranging from India's leading role in the non-aligned movement to our socialist government and close relationship with the Soviet Union.
US relations with Pakistan have largely continued into the 21st century, although they've soured a bit in recent years. Since the September 11, 2001 attacks, the US has provided Pakistan with about $28 billion in military and economic aid for the war against terrorism. Western officials claim that much of this aid has been misspent.
As for US-India ties, they have warmed considerably since then. Even inking civilian nuclear deals. But India continues to be allied with and purchases most of its military equipment from Russia, it refuses to abide by US sanctions, and has voted against US backed proposals at the UN. Most importantly, it refuses to give US corporations free reign within India. This makes for a largely ambiguous relationship. However, the US has become increasingly concerned about Chinese influence in the region, and sees India as a potential ally and crucial to countering and maintaining the balance of power in the region.
Therefore, while it is highly unlikely that the US, or China for that matter, would be in support of India in any confrontation with Pakistan, it is even less likely that the US would announce any support of Pakistan over India, as that would conflict with their long term interests. It seems that the neutral policy they've followed over the past decade will continue.