The Democrats regaining control of the US House of Representatives in the mid-term elections is unlikely to impact Indo-US relations, simply because the American system gives the President extensive leeway on foreign policy issues.
So while the Democrats in the House now might have the power to call for more hearings on issues like Russian interference in the US elections and President Donald Trump's tax returns, it may not be able to do much on issues vexing the Indo-US relations at the moment.
While the strategic relationship between the two nations has grown dramatically, with the US becoming India's second-largest weapons supplier and the country with which India has the largest number of annual bilateral military exercises, Trump's transactional nature has linked it with other issues like trade and immigration. These include tariffs imposed on Indian exports to the US, like steel, sanctions on Russia and Iran which directly impact India's purchase of weapons and oil from these nations, and plans to rescind work permits for H4-B visa holders, or the spouses of skilled immigrant workers.
After noting "the major bipartisan support we enjoy in the US," an Indian official said that "we are working out ways to resolve these issues." However, he admitted that " the Democrats winning Congress will not influence this all that much, because these are handled by the executive branch, or the Senate, where Trump is still King."
"On the strategic side, most key issues are relegated to Cabinet secretaries -- of Commerce or State, for example," Dhruva Jaishankar, Foreign Policy Fellow at Brookings India, told NPR. "Even if the Democrats take control of one or both houses of Congress and you have an embattled president, it might not make a difference for India."