Recently, there has been a lot on the shoulders of Shinjiro Koizumi.

In May, Mr. Koizumi, a 44-year-old scion of Japan’s long-ruling Liberal Democratic Party, was appointed head of the country’s agriculture ministry with a clear directive to reduce the price of rice — fast.

The Liberal Democrats were just two months away from a high-stakes parliamentary election. Polls suggested a poor showing. They also suggested that voters were acutely focused on a central issue: whether the government would be able to rein in skyrocketing prices of rice.

In recent weeks, while batting away comments from President Trump decrying Japanese rice import policies, Mr. Koizumi has scrambled to lower prices. Bags of rice from strategic stockpiles — costing less than half the price of other “brand” rices — have begun to hit grocery store shelves across Japan.

But ahead of the election on Sunday, polls still indicated that the ruling coalition was likely to struggle to retain its upper house majority as the rising cost of living fueled dissatisfaction with the status quo.

Such an outcome would thrust Japan into a period of political instability just before an Aug. 1 deadline to reach a trade agreement with the United States. If no such deal is reached, the Trump administration has said, the American ally will face a 25 percent tariff on all of its exports to the United States.