Prime Minister elect Tony Abbott is expected to look favourably on granting Tasmania a second minister in the new government, as recognition of the state party's victories.
Devonport-based Senator Richard Colbeck would be the most likely second minister.
He has done his apprenticeship as a parliamentary secretary in both government and opposition since 2004 and has rarely slipped up.
The Liberals have won Bass and Braddon and most likely Lyons, plus a chance of a third senate seat, based on estimates.
Hobart-based Senator Eric Abetz will automatically be a cabinet minister, and, as leader for the new government in the Senate he will be number three in the pecking order, after Mr Abbott, Liberal deputy opposition leader Julie Bishop and Nationals leader and new Deputy Prime Minister Warren Truss.
Labor had one minister, recently promoted to cabinet, in Hobart-based Julie Collins and outgoing Braddon MHR Sid Sidebottom as a parliamentary secretary.
In the Howard government the Tasmanian Liberals had a cabinet minister, Jocelyn Newman, while Senator Abetz was a junior minister.
On the Labor and Greens front, Premier Lara Giddings returns soon from her overseas trade mission, to a party and its Greens allies toxic with the electorate and with some tough work ahead of next March's state elections.
The Saturday swing against both parties was huge in Tasmania, topping 11 per cent for Labor in the two party preferred outcome after preferences.
The swings in Tasmania towered over the rebuff to Labor in other states.
Ms Collins survived only because of her popularity in Franklin. Her majority has been halved.
The Greens suffered a swing of more than eight per cent on primary vote in both Houses, although Senator Peter Whish-Wilson has a chance of holding on to the vacant seat he filled when former leader Bob Brown retired.