As of early 2018, the travel.state.gov website has been updated with a new URL and new wording about this, although the rules appear to be the same. It now says:
The visa expiration date is shown on the visa along with the visa issuance date. The time between visa issuance and expiration date is called your visa validity. The visa validity is the length of time you are permitted to travel to a port-of-entry in the United States.
Yes, the visa expiration date is the last day you can use that visa to apply to enter.
(As I just learned) A US Visa does not actually give you permission to enter the US, it just gives you permission to travel to a US Port of Entry and request permission to enter the US which can then be granted or denied by the immigration officer there. (Details)
The wording of that webpage implies that you can, indeed, travel to a port of entry on the expiration date, April 3rd. Of course if your flight is a little bit delayed and you arrive on April 4th all bets are off!
Edit not from OP: From travel.state.gov:
Comment not from OP
Although there is definitely ambiguity between 00:00 hours and 24:00 hours (ie start of first minute or end of last minute of the day) and I consider up to Tuesday to mean precisely on Monday or before visa authorities normally “play safe” (because of such ambiguity) and start and end dates are inclusive. In the insurance sector better consideration is given to this, for example 1/1/16 – 2/2/16 might have “bdi” appended, ie including both Jan 1 and Feb 2.
Credit:stackoverflow.com‘