On which switch position does it run? The first (next to off) routes the motor wire through a resistor, which is installed in your heater duct to help cool it. It could be the switch is bad and it's actually only running on LOW speed.
It should run on "high" "all the way" to the opposite side from "off."
66 shop manual, the closest I know of for free:
http://www.mymopar.com/downloads/servicemanuals/1966_Plymouth_Service_Manual.zip
Unfortunately the page numbers in this scan do not follow Mopar "dash" page numbers so you have to play with them to find what you want
"Heaters" starts about page 43 in your reader. Wiring diagrams, page 289
Valiant inst. panel wiring, page 302-303
At top of page 302 is the heater blower resistor, with wires C4 and C5 go off to the following page
to the blower switch, and a third wire, C1, runs off to the fuse in the panel.
What is NOT shown at the resistor is the left terminal is a two terminal connected buss, and the heater wire connects there.
The short end of this story is, you should be able to find the only wire going to the blower motor, pull it loose from the resistor, and jumper to a "good solid" battery source with a clip lead, and determine if the motor really will run at high speed, or if the bearings/ trash in the blower/ dragging blower is slowing it down, or whether problems with wiring/ fuse/ switch/ resistor is dropping the voltage