India was eager to start negotiating with President Trump over tariffs. Prime Minister Narendra Modi visited Washington right after the inauguration. Hopes were high for a quick trade agreement with a re-elected president who prizes deals.

Six months later, there is still no deal. With tariffs threatened and deadlines blown, India and the United States are up against a wall. On Friday, the United States is ready to impose a 26 percent tariff on all goods it imports from India.

Dozens of countries are facing the same imperative. But India, a democracy and the world’s most populous country, is a major commercial partner of the United States. Total trade between the two countries was roughly $130 billion last year.

The nations have deep cultural and demographic ties. Indian immigrants and Americans with Indian roots occupy a stratum of leadership roles in U.S. business, academia and politics.

Their economic ties are of vital and growing importance, to India especially. And for 25 years, Washington has been courting India as a military partner, sometimes explicitly as a counterweight to China.

Indian officials have been shuttling back and forth from New Delhi to Washington for months. On Thursday, India’s commerce minister, Piyush Goyal, told the Reuters news agency that the negotiators were “making fantastic progress.” There is the real prospect of talks going beyond this week. The Indian government has invited Mr. Trump to India for a defense summit in the fall, when Mr. Goyal has said he believes a bigger deal could be struck.