The question, therefore, is what the impact will be on India. Prime Minister Narendra Modi's recent trip to the United States was marked by a lot in terms of atmospherics, but not much that was concrete. Meanwhile, stresses in the relationship - in particular, on trade, on climate change and on intellectual property rights - continued to grow, with the prospects of their being addressed becoming even more remote. What will be the impact of the changes in the United States Congress?
It is important to note that, in many areas, the impact will, in fact, be positive. Defence and security co-operation will be one such. The senator overseeing the armed forces subcommittee will now be Senator John McCain, who is known to be a strong supporter of much closer relations between India and the United States, and between the militaries of the two countries. More hawkish voices on Pakistan-sponsored terrorism will also be in power now, which is likely to lead to more ears being turned to India's point of view on the dangers posed by international terror networks. It is also possible that energy-starved India will begin to benefit more from the United States' shale gas revolution - gas exports to India require special authorisation, and that could become easier under the new dispensation.
Still, there are some big dangers for the bilateral relationship, too. The biggest problem is likely to be on trade. The man tipped to be Senate majority leader from January, Mitch McConnell, was asked immediately after the election what policy domain is likely to see the closest co-operation between Republicans in Congress and the White House. He said it was trade. The United States president supports more trade-friendly policies than many in his Democratic party, and the Republicans might actually help him hammer out more trade deals than his own party did. This could go either way. It means that if India made a pro-active move to resolve the outstanding issues dividing the two parties at the World Trade Organization (WTO), the Obama administration might be emboldened to strike a deal. On the other hand, if India does not do so, and the WTO's Doha Round remains deadlocked, then the Republican majority will allow Mr Obama to move quickly on other regional trade deals that exclude India - the worst-case scenario for Indian exports. On intellectual property rights, too, the dangers of not reaching a deal have just escalated. In many ways, the pressure seems to be on India now.