There have been times in the past when there was very little ice trapped in glaciers. During this time, sea levels were higher because that water was in the ocean (most of it, anyway). It has been a long time since then. However, with global warming, more and more glacial ice is returning to the sea and this contributes to sea level rise.
The amount of fossil carbon that needs to be released into the atmosphere to cause most of the glacial ice to melt is not known. We can’t directly use ancient time periods to assess modern sea level rise by measuring the sea levels from those periods because there has been too much other stuff going on in ocean basins and along current coast lines. But, we can estimate that there was very little glacial ice during, for example, the early Eocene, and the transition of Carbon in the atmosphere to the formation of glaciers might be under 800 ppm. So, if we double the current amount of CO2 in the atmosphere, maybe that would melt all the glaciers. There was more methane in the air at that time as well, but we are releasing plenty of methane as we also release Carbon, so that’s not much of a problem. The biggest factor is probably this: The configuration of continents have changed since that time to increase the likelihood of glacial formation at the poles, so returning to some Eocene (or other) atmospheric CO2 value may result in much less melting. But that’s OK, because we can certainly increase the amount of carbon to more than around 800 ppm!
If we release CO2 at approximately modern rates (baed on population size), and have population increase up to a point, thus increasing CO2 release (in other words, do nothing significant to mitigate Carbon release, increase the number of people actively releasing it, and population goes up towards 8 or so billion) we can reach over 1000 ppm by 2300 AD, or sooner. That’s surely enough to melt most of the glaciers except bits and pieces in the coldest regions of Antarctica.
It is estimated (see this web page) that there is about 80 meters of ocean trapped in glacial ice. There are plenty of web sites out there that allow you to add ocean height to see how coastal regions would change, but the ones I know about don’t go to 80 meters. So, to find out what North America would look like, I found a map that has pixels to indicate altitude, with different colors representing topography, at a fine enough level to work with. This is the map, from here:
This map has a color coded key with elevations of 8, 54, 114, etc. labeled but there are color transitions half way between these marks, so there is a mark at 60 meters. I therefore will go ahead and assume that if most of the glacial ice melted, there would be a 60 meter rise in sea level. Therefore, a first approximation of what North America would look like with major glacial melting can be obtained by deleting all the bluish colors from 60 meters on down and converting them to ocean. The resulting map looks like this:
There are several caveats. First, sea level would not rise uniformly, but rather, it would go up more in some places than in others. In the US, I think there would be more sea level rise along the east coast, father to the south, because of a number of these effects, so where you see a coastal plain remaining along the eastern mountains, maybe delete that; perhaps the shores of the Atlantic would wash against the Appalachians or Piedmont in Virginia and North and South Carolina. Also, as sea level rises, the land will be pushed down various amounts by the weight of the water, so this might be considered a minimum estimate of rise in some areas. Also, erosion would cause important changes. If you look at, say, a 60 meter topo line in a region made of something other than hard rock, you have to assume that transgression of the sea including the effects of erosion would move way inland in some cases. Also, this map has the edge of the continent all rough and wiggly. This would only be true where hard bedrock meets the sea. Other places, there would be smoothing off, formation of linear barrier beaches, and the rise of deltas.
But putting all that aside, there are some amazing effects. For one thing, the Atlantic extends to and engulfs Lake Ontario. Also, it appears that the Hudson and Champlain valleys merge and join the Saint Lawrence Seaway, so New England and adjoining regions of Canada become a big rocky island. The region of New Orleans and the Lower Mississippi become a large embayment, with the southern end of the Appalachians and nearby mountains forming a peninsula.
El Centro and the Salton Sea become part of the much enlarged Baja (Sea of California). Hudson Bay gets huger. Ignore Greenland; that big ocean in the middle of Greenland would mostly rise up and become land, as this area is currently depressed by glacial mass. Also, gee, there seems to be a big ocean in Mexico.
This is a VERY ROUGH approximation. Just for fun.
The image at the top of the post is from NOAA and shows, I think 10 meter sea level rise from a different angle.