I can’t name the construct, but I’ll explain its meaning; maybe that will help.
The likeliest meaning is seen if we replace ”with” with ”because it will result in” :
This may not pose an immediate problem but its long-term effect could be disastrous because it will result in the country needing more and more food grains to support its growing population.
or, further expanding the last part of the sentence:
This may not pose an immediate problem but its long-term effect could be disastrous because it will result in the country finding itself in the situation where it needs more and more food grains to support its growing population.
The above (either of them -- their meaning is identical) is, as I say, the likeliest meaning and it's probably the one the author intended. But there is an alternative, albeit less likely interpretation. It can be seen if we replace ”with” with ”in light of” :
This may not pose an immediate problem but its long-term effect could be disastrous in light of the country needing more and more food grains to support its growing population.
or, again further expanding the last part of the sentence (and, for clarity, a little change to the prior part too):
This may not pose an immediate problem but its long-term effect could be disastrous in light of the fact that the country is already in the situation where it needs more and more food grains to support its growing population.