For more than a year, a Czech program that scours the world for ammunition has been a crucial supply line for Ukrainian forces desperately in need of artillery.

But little is publicly known about the program, and its opacity may be its undoing.

If an opposition populist party prevails in this week’s parliamentary elections in the Czech Republic — as it appears poised to do — its leaders have vowed either to disband the ammunition program or to ask NATO to run it so they can concentrate on the country’s wobbly economy.

With consumer prices rising, “obviously people are getting more and more nervous,” said Jaroslav Bzoch, a member of the European Parliament from the populist party, Ano. The party has derided the ammunition program not just as overpriced but also as opaque because of its reliance on shadowy business deals.

Other NATO nations have already recalibrated military spending in the face of war-weary publics that want to focus on domestic priorities. At the same time, Ukraine depends heavily on Western military support, and Russia is pressing forward with the war, trying to seize as much Ukrainian land as it can.

Officials and experts said the ammunition program, which relies on billions of dollars in donations from NATO countries, costs Czech taxpayers relatively little. But even the perception that it could further bog down the economy has stuck with voters who Mr. Bzoch said were already skeptical of the program.