The first on Wednesday is a must-win for a government that has shed cabinet ministers over the last year amid leadership struggles and a slide in the polls.
Voters will cast ballots in the Tory stronghold of Conception Bay South, west of St. John's and adjacent to the premier's Topsail district.
"It is right next door and it's an important byelection for us," Davis said Tuesday of his first showdown at the polls as leader.
"One of the disadvantages if you like, or the challenges, is that I'm still very new to this office. It takes a long time for people to have an opportunity to identify with a new government, a new leader, and see how I'm going to operate."
The Tory government has held majority power since 2003. But it has lost four straight byelections to the Opposition Liberals in the last 16 months, three of them in districts formerly held by senior cabinet ministers.
Provincial law requires Davis to call a general election within a year of the date he was sworn in as premier on Sept. 26.
Conception Bay South was held by former justice minister Terry French, who resigned in September to return to the private sector. He won the district in a byelection in 2002 after the death of his father, Bob French, who had represented the Tories from 1996 until he died.
The premier's effort to revive party support is riding on what happens in that district, said former Tory cabinet minister Shawn Skinner.
Success or failure in Conception Bay South (CBS) will set the stage for two more byelections later this month, he said in an interview.
"I think a win in CBS will be helpful to both, and will give us a decent shot at winning both of those. A loss in CBS, I think, will be disastrous. I have to be honest."
Voters will cast ballots Nov. 25 in the Humber East and Trinity-Bay de Verde districts.
Skinner said even with a victory in Conception Bay South, those byelections will be hard fought.
"I would suggest to you that they're going to be tough seats to win."
Humber East and Trinity-Bay de Verde were held by former premier Tom Marshall and former finance minister Charlene Johnson, respectively. Marshall retired from politics while Johnson resigned to be with her husband who works overseas.
Christopher Dunn, a political scientist at Memorial University of Newfoundland, said if the Liberals pick up another seat it will probably be in Trinity-Bay de Verde.
"The other two, I wouldn't expect to change party colours," he said in an interview. "And if they do, it's a disastrous scenario for the (Progressive) Conservative government.
"Pack up your bags, guys. It's time to call it a day. That would be an awful situation, I think, for them."
Aside from the three vacant seats, there are 29 Progressive Conservative members, 13 Liberals and three NDP members.
Follow @suebailey on Twitter.Suggest a correction