Polling institute gfs.bern found 53 percent of those surveyed supported the increase, which would take effect in 2016, although six percent were undecided, the results released late last week showed.
Voters will decide the issue on November 24th.
The motorway tax has remained unchanged since 1995 despite a doubling of traffic on Swiss roads.
All motorists using Swiss motorways are required to buy a windscreen sticker even if they are tourists passing through the country.
Under the proposed change, backed by the government, visitors would be able to buy a sticker or “vignette” valid for two months for 40 francs.
Opponents, including the right-wing Swiss People’s Party and the Touring Club Schweiz (TCS) motorists’ group, regard the 150 percent tax increase for the annual pass as a swindle.
They argue that the government is already raking in nine billion francs a year from the existing tax but only 30 percent goes back into road maintenance and construction.
The rest goes into government coffers or to finance public transport.
Critics say revenues from the higher tax won’t do anything to resolve traffic jams in densely populated areas such as the Lake Geneva region and around Zurich.
The government and supporters of the hike say that, in fact, the revenue goes into a special fund for dealing with motorway traffic.
The extra revenue will finance needed bypasses at Morges, west of Lausanne in the canton of Vaud, at La Chaux-de-Fonds, in the canton of Neuchâtel, and at Näfels in the canton of Glarus.
It will allow federal authorities to take over 400 kilometres of roads from the cantons and to ensure that all major cantonal centres are hooked up to the motorway network.
A “no” vote will block expansion of the network and more than four billion francs’ worth of projects for the next 20 years, the government says.
Green parties from both the left and right oppose the tax increase because they are against any expansion of the road network, preferring to see money ploughed into the public transport system.
Most parties are supporting the increase, although the Social Democrats have yet to take an official position, something they are set to do at the end of the week, the ATS news agency reported.