Ukrainian President Petro Poroshenko appeared before the U.S. Congress last September and pleaded for weapons to counter Russian advances. Afterward, members of his delegation sat down with two American supporters at a home in Georgetown. Why, the Ukrainians asked, was the Obama administration promising so much but doing so little?

Michael Pillsbury, a Pentagon consultant, and Gordon Humphrey, a former Republican U.S. senator, leaned across a white couch and whispered to each other. It was just like 1984, they agreed.

Few Americans have more expertise pushing a balky administration to battle an invading Russian army than Messrs. Pillsbury and Humphrey. In the mid-1980s, having concluded President Ronald Reagan wasn’t serious about arming the Afghan mujahedeen, they worked with Rep. Charlie Wilson to build the largest covert-action program in Central Intelligence Agency history. The Soviet army, stung by the advanced U.S. weaponry provided to local forces, withdrew from Afghanistan in 1989. The Soviet Union collapsed soon after.

Today, as the two Cold War adversaries face off anew, it is the Ukrainians who are desperate for U.S. weaponry and struggling to make sense of U.S. policy. Members of the coalition that prodded Mr. Reagan into fighting the Soviets in Afghanistan have reopened their 30-year-old playbook, this time seeking to pressure President Barack Obama to punch back against Vladimir Putin’s Russia.

This account of their effort is based on interviews with Messrs. Pillsbury and Humphrey and many others involved, including administration and defense officials and the visiting Ukrainians.