American officials had expressed concerns to New Delhi about the thwarted plan to kill the man, who is a U.S. citizen. The plot that prosecutors described resembled a June assassination in Canada.
A war with who? The US? Not a chance that happens over something like this. What would the US' achievable war aims even be that could possibly justify the human and economic costs of a war with India? And I mean that both ways; not only how many American military deaths would the US be willing to incur just to make a point about their sovereignty but how many Indian casualties would the US be willing to inflict over the state-sanctioned murder of one non-US citizen on their territory? How many would be appropriate? I would submit that the most rational and likely answer is none.
Most "acts of war" don't start wars. At worst the US would probably impose sanctions against the Indian government officials they believed were involved. Given how much they want India as a partner to blunt China it would more likely be strongly worded statements of condemnation and back room tut-tutting. The US isn't going to fight a war against one of their top 10 trading partners and disrupt maritime shipping in the Indian Ocean over the murder of a foreign dissident on American soil.
With India, no, but India is dependent on Western military imports to replace it's aging Russian equipment to deter the Chinese and Pakistan joint threat. Those deliveries can be shut down due to these actions, leaving India very week and prone to attack.