A general rule, the more an appeal tugs at your emotions the less likely it is supported by logic.
Rising sea levels should be a consequence of a warming world. As oceans and the atmosphere warm, water expands and the melting of glaciers and icecaps should increase causing sea level rise around the world. In any one location there may be complications of vertical land movements and changes in winds, salinity and currents causing aberrant measurements but if enough sites are measured, a consistent pattern of sea level rise should emerge.
In a previous article I calculated sea level rises for many tide gauges along the coasts of Western North America, Eastern North America and Europe, correcting the measured sea levels for vertical land movements. Here I have combined the sea level rises for these 83 tide gauges to try to calculate the best global estimate.
Here are the 83 different tide gauges:

From the graph, the average and median values are in close agreement with an average increase in sea level of 1.79 mm per year with a standard deviation of 1.12 mm. With 95% confidence this puts the value of sea level rise somewhere between a decrease of -0.45 mm/a to an increase of 4.03 mm/a.
If the increase is actually 1.8 mm/a and the rise continues to be as constant as it has been for the past 100 years it will take 555 years for the sea level to rise 1.0 meters (39.4 inches). If the high estimate of 4.0 mm/a is used, it will take 250 years to increase by 1.0 m.
The values of sea level rise can also be compared using a histogram. In this histogram the sea level rises are grouped into 0.25 mm increments.

The greatest number of sea level rise measures are in the 1.25-1.50 mm increment with 18 of the 83 tide gauges. The second highest number is for the 13 tide gauges in the 1.50-1.75 increment. Few gauges measure sea level rise at less than 1.25 mm/a or more than 3.0 mm/a.
With an estimate of 2.0 mm/a for sea level rise it will be another 5000 years before the Statue of Liberty is swamped. Probably long melted down and beaten into swords by then, a useless relic of a bygone age where primitive men believed in quaint notions of liberty and freedoms.
Just for reference, this is the observed sea level rise around the Statue of Liberty over 120 years:

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