If you wanted to 'go Dutch' on this then it would mean a total transformation of the environment, basically a ring around all of the Marshall Islands anchored to the sea bed. But that would transform the whole thing into a sweetwater archipelago in no time and would likely kill off everything inside it.
This is more or less what happened to an inland sea that we had here, it's now a lake and sweet (IJsselmeer).
The last 3,000 years of human habitation on those islands would suggest that this is not one of those places.
Because that's clearly true. All of those old strip mines, and Superfund sites, and nuclear test sites, and the region around Chernobyl, and the former fishing towns of the Aral Sea are trivial examples of how sites have been rendered less fit for human habitation.
However, that logic of the argument is a bit silly, since it sets aside considering how human agency may be responsible for the removal of that part of the human ecosystem.
There really are places which "are simply not fit for human habitation" include the top of Mt. Everest, effectively all of Antarctica (the few highly subsidized settlements not withstanding), and a number of small islands (like Bishop Rock). The Marshall Islands do not fit into that category.
Like all atolls, it's a very thin circle enclosing a lagoon. By my estimate it's about 100 meters wide, from ocean shore to lagoon shore.
As a very rough estimate, 1 meter of dike height needs 3 meters of surface, so 6% of the island will be a dike. The Dutch can do this because their dikes enclose a lot of land. That's not possible here.
The Dutch also have good soil and rainfall. The ground of the Marshall Islands is made of porous coral. aaron695 elsewhere in these comments pointed to a NatGeo article at http://news.nationalgeographic.com/2015/02/150213-tuvalu-sop... . Towards the bottom is a picture with the caption 'Flooding during king tides is a problem on Fongafale, when water percolating up through the coral matrix laps even at the door of the meteorological office.'
Thus, dikes won't prevent salt water from percolating through the coral under the dikes and flooding the other side.