If you have water pressure under the house, plugging the holes will just try to float the house! The pressure will increase, and the flow with it. The fact the pump runs so much is a function of the flow rate. Unless you can drain some of that water away some other way, plugging the holes will likely just cause the water to seep in through imperfections in the floor and walls.
NO, plugging some holes is not the answer. Maybe drainage around the foundation on the outside might help, but you need some place to drain it to. If you don't, then you'll have to pump it. Now, if you are just dumping that water on the ground outside, you might be pumping it continuously...make sure where ever you pump it to, it can drain away from the foundation.
The house I grew up in would fill the entire basement in about 4-hours a foot deep if the power went off in the spring. The pump ran quite a bit, probably more than yours. If you can't move it away from the foundation, either live with it or move the house or yourself. Sealing the foundation can quite literally crack the foundation from the pressure...houses typically aren't very good boats.