Given the bipartisan support and evolving "strategic partnership" between the two democracies, India barely figured during the election campaign. Outsourcing and visas were mentioned but as a glancing reference as part of the poll rhetoric.
Mr Obama has said India figures "big" in his plans, but it is not clear how and in what way he would direct US policy towards India in the next four years. A host of experts and US-based think tanks have suggested a "to-do" list as he prepares to announce his policy priorities in the inauguration address on Monday and the State of the Union address next month.
Some observers believe "pragmatic" Obama's second term would not differ radically from the first and US-India relations would be deepened with some new initiatives.
Others say factors like the discovery of shale oil and gas providing the US with a strategic boost will influence its global relations and there could be a redefining of the notions of engagement. Outgoing Secretary of State Hillary Clinton has already spoken about the new means of diplomacy, what she called "smart power" that includes trade, technology and private investment, to advance US interests.
And change has been a recurring motif with Mr Obama as evidenced in the slogans of "the change we believe in" in 2008 and "forward" in 2012. It is believed that the president would be thinking of his legacy as previous re-elected presidents had pursued international initiatives. It is therefore natural to expect some new issues and priorities that will shape US relations with the world and India.
One such issue is global trade. The year 2013 is going to be quite an important year since 2001, when the Doha Round was launched and China joined the World Trade Organisation. By the end of this year, new WTO negotiations would begin on liberalising trade in services such as consulting, banking and insurance, and on expanding the 1996 Information Technology Agreement that eliminated tariffs on trade in devices like memory chips. These talks are likely to produce the biggest negotiated liberalisation of trade since the Uruguay Round of early 1990s.
At the same time, negotiations could be completed on the first trans-Pacific free trade agreement and started on a trans-Atlantic deal between the US and the EU.
India had a glimpse of US trade agenda earlier this month when Mike Froman, an Obama administration adviser and possibly the new US Trade Representative (USTR), said the world has "turned the page" on Doha and indicated that the Trans-Pacific Partnership (TPP) would be pushed as an alternative.
According to Mr Froman, major emerging countries like India and Brazil want to maintain their developing country status and do not want to open their markets. Mr Froman has also charged India with blocking a trade facilitation agreement on infrastructure at ports and custom stations.
The US and other developed countries have also begun pushing for "early harvest" agreements - the plurilateral or select group agreements on goods and services - ahead of the next WTO ministerial meet at Bali in December as the Doha Round is stalled.
The Obama administration has also signalled it would be push forward the New Silk Road concept mooted by Clinton -- an international infrastructure network that would remove barriers to flow of goods and people among countries of South Asia.
Robert D. Hormats, Under Secretary of State for Economic Growth, Energy and Environment, has spoken of an Indo-Pacific Corridor that would reach out to Southeast Asia, making the region a hub of global trade.
There is a strategic angle to this. Following the pullout from Iraq, and planned drawdown of troops from Afghanistan by the end of 2014 and China's growing assertiveness in East and South China Sea, Mr Obama has been reorienting US policy towards Asia-Pacific.
Some believe the US interest in making India an anchor country for regional economic cooperation is aimed at gaining New Delhi's support for facilitating its exit from Afghanistan. Hormat has indicated that success of Afghanistan would depend on the level of regional cooperation.
The US has made a "bet" on India and would perhaps shape the context in which India would take its decisions. In Mr Obama's first term, joint initiatives in areas like energy and healthcare were launched. In the second, both countries could collaborate on maritime and cyber security.
However, it is felt that the Obama administration has failed to develop a sustained policy helping India achieve its economic and security goals. Obama has belied Indian hopes of US pushing reforms at the IMF and World Bank that would give its voice greater weightage on international fora. And a renewed move for the Comprehensive Test Ban Treaty (CTBT) would only create more strain.