City boosters in this Nordic capital dream of a Guggenheim museum of Finnish wood rising near the Baltic Sea and one day drawing millions of tourists and cruise passengers. But the huge costs of the proposed development are stirring a backlash here against an institution that is ordinarily accustomed to eager suitors.

The proposal for the city of Helsinki to team up with the Solomon R. Guggenheim Foundation in New York to build a museum here is splitting politicians into camps of pro-business supporters seeking the wealth and attention that comes with an international brand, and Social Democrats and other left-of-center party members who are skeptical about shouldering the costs of a 130 million euro ($177 million) development deal.