BOZEMAN, Mont. — Rob Quist surveyed his audience last week at an annual powwow of Montana’s Native American tribes, a kaleidoscope of feathers, moccasins and beads, before turning his thoughts to a very different audience, far to the east: the national Democratic Party.

“They’ve been on the sidelines a little too long, and it’s time for them to get in the game,” said Mr. Quist, the banjo-playing Democratic nominee in a special May election to fill Montana’s at-large House seat.

But, he predicted, “they’re coming in.”

They may have little choice. After a hard-fought campaign to fill a House seat in the Atlanta suburbs fell just short of outright victory on Tuesday, the House seat in Montana vacated by Interior Secretary Ryan Zinke is up next, and a groundswell of new activism on the left is demanding attention.

Democrats have now chalked up a closer-than-expected loss in a House special election in Kansas this month and a near miss in Georgia, leading logically to discussions of how hard to play going forward — not only in the June 20 runoff between their first-time candidate Jon Ossoff and the Republican Karen Handel in Georgia, but also in looming House races in Montana and South Carolina.