While it has drawn far less interest than a special House election in Georgia, the Montana race is drawing the attention of both parties. Senator Steve Daines of Montana announced on the call that Vice President Mike Pence would campaign with Mr. Gianforte, setting up something of a proxy fight between the administration and Senator Bernie Sanders of Vermont, who is set to stump later this month with the Democratic nominee, Rob Quist.

Republican groups, alarmed by the intensity of liberal voters during special elections this year, have been pouring millions into the state. National Democrats have been skeptical about the prospects of Mr. Quist, a folk singer-turned-novice candidate who has been battered by stories about his personal finances. But the House Democratic campaign arm has been nudged to put money into the race.

Mr. Quist has raised more than $2 million, in large part because of liberal online donors — a fact that Mr. Gianforte highlighted on the Thursday call.

“The Democrats have fired up this ActBlue organization,” he said on an audio recording obtained by The New York Times, referring to the online Democratic fund-raising hub. “We’re seeing about $70,000 a day pouring into the state from liberals in San Francisco, New York and Hollywood.”

Asking the lobbyists to give $5,000 each by Friday to “scare off some other Democrat money,” Mr. Gianforte acknowledged that Mr. Quist had far wider support.

“We’ve had over 5,000 individual people support the campaign financially so far,” he said on the recording. “The challenge is my opponent has over 30,000 contributors.”