The party remains Switzerland's largest, despite a drop in support in October legislative elections, and currently has just one seat while smaller parties have two.
The Federal Assembly is meeting from 8am for the vote that takes place once every four years and that will see ministers re-elected or replaced.
Among them is foreign minister and current president Micheline Calmy-Rey of the Social Democrats who is stepping down.
The country's five largest parties have held intense discussions in recent weeks as they aim to hold onto their seats while keeping intact the so-called "magic formula" or power-sharing agreement.
Until 2003 the seven posts were allotted to the four biggest parties -- two seats each for the centre-right Liberals, centre-right Christian Democrats and the centre-left Social Democrats, with the remaining portfolio going to the SVP.
That year the SVP gained a second seat at the expense of Christian Democrats only to lose it after the 2007 election when their candidate joined the newly-formed Conservative Democrats.
The Federal Assembly votes in a secret ballot of several rounds.
Any eligible candidate can receive votes in the first two rounds but subsequently the person receiving the fewest votes is removed from the race until one candidate gains an absolute majority.
The parliament then moves to elect a chancellor, president and vice president.
The next government will enter into office amid concerns over a slowing economy.
While Switzerland is relatively cushioned against the kind of debt problems that have beset eurozone nations, it is suffering from the fallout.
Its economy is highly dependent on exports, which are suffering as demand drops in Europe.
This is exacerbated by the relative strength of the Swiss franc against the euro and the dollar.
The government on Tuesday cut its 2012 growth forecast to 0.5 percent from 0.9 percent, citing the eurozone crisis as a factor.