PANAMA CITY – Squeezing the hulking container ships known as “Panamaxes” into the Panama Canal’s Miraflores Locks requires a marvel of precision steering and patience.

The ships top out at 965 feet long and 106 feet across, leaving only two feet of wiggle room on each side. As many as four pilots employed by the canal must jump on board to help ship captains get through without shredding their vessels’ hulls or crushing the 92-year-old locks.

Built to comfortably accommodate the biggest ships of their day, the locks are feeling awfully snug these days. The waistlines of the world’s shipping fleet have swelled so much that the biggest new ships simply can’t wedge through Miraflores anymore; instead, they have to find another route.

All that lost business – and the prospect of more – has made Panama jumpy enough that it wants to spend $5 billion or more to dig three parallel shipping channels and build two sets of enormous new locks, which lift and lower ships to overcome the differences in elevation on the route between Panama’s Atlantic and Pacific coasts.

But there’s a catch. By law, Panamanian voters will get the final say on the project in an election Sunday, the first test of the public’s confidence in canal administrators since the United States turned over control in 1999. After months of campaigning, the referendum is highlighting the role the canal plays in shaping this small country’s future and its identity.

“Americans have the Statue of Liberty, the French have the Eiffel Tower, Panamanians have the canal,” said Leopoldo Neira, a Panama City pollster. “The country’s identity is wrapped up in the canal.”

The authority’s strategy, though, seems to be working, easily overcoming a fractured and poorly funded opposition that has tried to convince voters that Panama’s endemic corruption would eat up any profits generated by the expansion. Neira’s latest poll for La Prensa newspaper shows 68 percent of Panamanians support the expansion proposal.

The proposal now calls for new 180-foot-wide, 1,400-foot-long locks on the Atlantic and Pacific sides of the canal that would dwarf the current 110-foot-wide, 1,000-foot-long locks. Crews would also dig nearly seven miles of shipping channels to connect the locks with the 50-mile canal, as well as deepen Gatun Lake, which serves as a reservoir.

The work, which is also intended to lessen bottlenecks that keep some ships waiting offshore for four days before they can enter the canal, would be paid for by a 3.5 percent increase in tolls.