While much of the focus has been on Khobragade, the cause of the nanny, Sangeeta Richard, has been taken up by a non-government organization called Safe Horizon, which campaigns for victims of abuse.
It said that although Richard's legal presence in the United States was tied to her employment, she had been granted temporary permission to remain while she cooperates with law enforcement as a victim of human trafficking.
It said Richard was likely to apply for a special "T-1" visa reserved for trafficking victims. Such a visa would be valid for up to four years and allow her to work in the United States. It can also lead to lawful permanent residence, according to the website of U.S. Immigration and Customs Enforcement.
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Khobragade's departure would remove the focus of current friction between New Delhi and Washington, but it is unclear how long it will take the anger to subside in the run-up to national elections in India in May. Also, the continued presence of Richard in the United States could prove an irritant.
The case has exposed underlying problems in a bilateral relationship that has failed to live up to its billing by President Barack Obama in 2010 as "a defining partnership for the 21st Century."
Critics accuse Obama of failing to pay sufficient attention to ties with a country viewed as a key strategic counterbalance to China and as an engine to boost the U.S. economy, while American hopes of building a more robust business relationship with India have run into bureaucratic hurdles.
Frustration has grown among the U.S. corporate lobby. Indian sourcing rules for retail, information technology, medicine and clean energy products are contentious and U.S. firms complain about "unfair" imports from India of everything from shrimp to steel pipes. In June, more than 170 U.S. lawmakers signed a letter to Obama about Indian policies they said threatened U.S. jobs.
Daniel Markey, senior fellow for India, Pakistan and South Asia at the Council on Foreign Relations, said the Khobragade case made it appear the Obama administration had taken its eye off the ball on the relationship with India.
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"The question is why this wasn't managed in a more sophisticated or subtle way, because things can be managed more effectively. This was always going to be an issue, but it could have been resolved more rapidly with less fanfare."
Speaking at a seminar on Thursday, Ron Somers, president of the U.S.-India Business Council blamed "bumbling on both sides" for the Khobragade affair.
"We have to do some thinking on this side as to what has there been in the way of frustration that allowed this incident to provoke and spill over as it has," he said.
"We really need now to be building trust and taking an introspective look at whether we really mean what we say when we talk about strategic partnership and how do we get there."