They support the construction because Prior to this, long-distance travel was slow, and the spread of goods and information was nearly nonexistent between faraway states.
This make it difficult for producer such as farmers to distribute their products and sell it other people outside their area.
The Development of transcontinental railroad cut down both the cost of production and the time of delivery of the farmers. On top of that, the construction also provides a lof of labor jobs for the people.