I believe the idea is to make a coin with a face value of $1 trillion, not a coin worth $1 trillion, which is why this is baffling to me.
No, the best I can tell, the idea is to make the coin legal tender, in which case it would definitely be worth $1 trillion.
Although there are some people who insist that the constitution only allows Congress to mint currency fully backed by gold or silver, in reality Congress has the power to mint currency without raising debt. This is called seigniorage
This still happens on a small scale when, for example, the U.S. Mint creates and sells sets of commemorative quarters for the 50 states, as the U.S. Treasury estimates that it has earned about $6.3 billion from these since it launched the program in 1999.
Many moons ago, I tried to explain to people how having the U.S. Treasury print money to pay down federal debt would have very different effects on debt, taxes, and inflation, than having the Federal Reserve print money, although one poster around here insisted there would be no monetary difference, besides the fact that Congressmen would be making the decision rather than the Fed (which isn't even true, as the U.S. Treasury & Mint could become just as insulated from Congress as the Fed is now, if need be).