I have a converter that outputs 5v and 1 amp. The input voltage can be 2.5-6 volts. Does it matter as long as it is in the range? Also, will the current draw from the batteries differ if I change the input voltage? Here is the link to the usb converter: http://www.ebay.com/itm/261097668334?euid=cbb7b0f1c6c84804827dc94d84ad2d39&cp=1.
If your source (batteries?) can deliver the required power, it doesn't matter what the input voltage is as long as it's in the range. The current draw from the batteries will be higher as the voltage gets lower for a constant output load.
A DC-DC converter with a constant output load is a constant power device. In your case your converter puts out 5W (5V*1A). There are some conversion losses, so the input power will be higher, for example maybe 6W (the output power divided by the efficiency.)
So your input must supply 6 watts. At 6 volts that will be 1A. At 3V that will be 2A, etc.