His campaign manager, Ravo Root, is a high school friend — “We were in band together,” Mr. Morgan said — who is still in college in Potsdam, N.Y., some 300 miles from the district.

The seat that Mr. Morgan is trying to win is a comfortably conservative one, most recently represented by the former senator Catharine Young, a Republican.

Ms. Young stepped down in March after failing to oust the minority leader, Senator John J. Flanagan of Long Island, following the party’s devastating losses in 2018. Those losses flipped Albany’s upper chamber to Democratic control for only the third time in the last 50 years.

But Republicans are seemingly not taking the seat for granted; the Republican State Senate campaign has spent $90,000 to assist their candidate, George Borrello, something Mr. Morgan sees as a sign of nerves.

If Mr. Morgan were to win, it would be a resounding upset, and perhaps reflective of how the impeachment-related developments surrounding President Trump have filtered down to local races. That possibility, Republicans say, is exceedingly dim.

“George Borrello is an extraordinary public servant and we are confident he will win resoundingly on Tuesday,” said Scott Reif, a spokesman for the Republican minority in the Senate.

The race in Monroe County, where registered Democrats outnumber Republicans, may be a closer call. That Democratic advantage is also the case in Ulster County, in the Hudson Valley, where Mr. Soros’s PAC, the New York Justice and Public Safety Political Action Committee, has also put at least $184,000 behind Democrat David Clegg, who is running against Michael J. Kavanagh, a Republican.