Seeing is believing for donors to the new Miami Art Museum now under construction alongside Biscayne Bay in downtown’s Bicentennial Park.

With elevated platforms resting atop columns, a trellis-like roof, and a grand staircase that opens onto the water’s edge, the MAM building designed by the Swiss firm of Herzog & de Meuron has generated enthusiasm among architectural critics and museum officials alike.

Lately, MAM director Thom Collins said, that sense of excitement has spread to the museum’s benefactors.

As workers give shape to the museum’s Stiltsville-inspired design, donations to the building campaign are on pace to meet the promise made by museum trustees to raise $120 million in private funds to offset the costs of construction and future operations, he said. More than half has already been pledged.

“People don’t get on board until they see things,’’ Collins said during a recent tour of the construction site. “We’re well within $2 million of finishing the bricks and mortar fundraising.’’

Collins said he is much more relaxed these days than he was last December, when it was announced that upon completion of the building in fall 2013, MAM would be renamed the Jorge M. Perez Art Museum of Miami-Dade County, or PAMM for short, in exchange for a donation of $35 million from the Miami real estate developer.

The community response was divided among those who congratulated the museum and Perez on the generosity of his gift, and those who criticized the name change for giving one person all the credit for a museum built largely with public money approved by Miami-Dade voters in 2004.

In fact, MAM will need even more public support when the new building opens because operational costs are projected to more than double from the present $4 million a year to about $10 million. Currently, MAM relies on about $2 million a year in public funds to cover the costs of exhibitions, educational programs and staff.

Many warned that the museum’s name change would hurt future private donations, which help offset those operating costs, by sending the unintended message that the institution is taken care of.

“Bringing money in is going to be harder,’’ said Miami collector Carlos de la Cruz, who along with his wife, Rosa, runs the De la Cruz Collection Contemporary Art Space in the Design District. “I think that’s incontrovertible.’’

But nearly one year since the announcement, said MAM’s board chairman, Aaron Podhurst, the fundraising campaign is riding the momentum of its unmistakable landmark rising from the ground.

“Now we’re getting excitement,’’ he said, “and we’re trying to get some of the big gifts in.’’

Yet the work of fundraising for any cultural nonprofit, he added, “never stops.’’

The guaranteed maximum price for MAM’s new building is $131 million, Collins said, but the total price tag on the project, including an endowment to ensure its future operations, is about $220 million.

Public money from a general obligation bond approved by Miami-Dade voters in 2004 will pay $100 million of that cost. Museum trustees pledged to raise an additional $120 million in private donations, including $31 million to offset construction costs, $70 million for an endowment to ensure future operations, and $19 million for transitional expenses.