The way that the gold standard ties the value of a dollar to gold is usually by making a dollar exchangeable for a fixed amount of gold. For example, from 1934 until 1971 the US government would exchange \$1 for 1/35th of an ounce of gold.
One of the charms of using gold as a currency is that it is durable and extremely valuable for how much room it takes up. How would anyone actually implement monetary conversion for Big Macs? Would there be a Fort Kroc where 3 billion Big Macs (worth the \$11 billion of the current US Gold stockpiles) would be kept? The same perishability and low value per unit volume of make Big Macs delicious meals to millions also make them a terrible anchor for a commodity currency.
It is true that consumption of gold services in the form of gold jewelry and the like make demand for gold pro-cyclical. But empirically, prices were stable and inflation low during the gold standard. Therefore it is hard to imagine this was a severe problem. Of course, the gold standard has lots of problems including:
- The supply of gold increases slowly over time relative to the economy, leading to gradual deflation which is thought to make recessions worse.
- The use of gold as a backing for currency significantly increased demand for gold, leading to tremendous diversion of resources into gold production.
- Like any pegged currency, a gold standard depends on reserves which can be exhausted in a panic about the future ability of a government to convert.
Big Macs might not suffer from all these problems but, as mentioned above, suffer from lots of other problems that make it problematic to use them as or a backing for money. And how would you handle counterfeiting?
One reason all major counties have moved to fiat money is that it doesn't suffer from any of the problems of gold listed above. It also doesn't suffer from the additional weaknesses of Big Mac being both perishable and a low value item.
One negative of fiat money is that the monetary authority (e. g. the central bank) can't abuse their discretion to create high inflation. But Big Macs suffer from this problem too. Because Big Macs are easy to create in large quantities and short run demand is relatively inelastic, the government could create lots of inflation by just grilling up their own, just as they could run their printing presses.
Yes, it is true that consumers of Big Macs are probably poorer on average, and so they would benefit relatively more from cheaper burgers if the government tried to inflate away the debt by printing money (grilling up burgers) but even if they were free how many would people eat? That's why their demand is inelastic, people don't want that fourth burger in one day nor do they want to eat them everyday forever. As for the other costs of higher inflation, that's a more complex issue and probably best posed as another question about what are the benefits and costs of higher inflation and who gets what. But original question asks would it be workable. The costs of conversion to a commodity backed money based on Big Macs seem to have little to recommend it and enormous costs both in transition off fiat money, governance (counterfeiting and monetary policy), and ongoing implementation owing to low value per item and perishability.