If you're talking about pre-Reaganomics, you're basically talking about Keynesian economics, i.e. policies focused on demand side economics (Reaganomics focuses on supply side economics). Those policies don't necessarily equate to higher wages in general and they certainly don't equate to higher wages for fast food employees because the policies focus on addressing real value wages rather than nominal value wages. The latter is the actual dollar amount while the former is the spending power that individual wage income represents. An example of how real value would be increased is by increased government spending on infrastructure and social welfare.
If I make $20k a year but the government invests in infrastructure such that my mass transit costs (subway, bus) are static rather than increasing substantially over the course of a few years that's more money I can spend in the consumer market to stimulate the economy. Similarly if a free or afforable subsidized health care clinic opens up in my neighborhood and/or there is real government subsidized free healthcare, that is also more money I can now spend in the stream of commerce. Investing in infrastructure also means increased employment in building, maintaining, and/or upgrading that infrastructure, i.e job creation at wages better than minimum wage.
Aside from fiscal policy, there's also monetary policy, which is already largely in place in the form of lowered interest rates. That's going to gradually change over time and is a current hot button topic in terms of what's going on at the Federal Reserve. In theory by lowering federal interest rates, banks and other financial institutions are more likely to extend credit to businesses to stimulate business growth which can lead to increased employment and increased wages.
While all of this has the potential to create better employment opportunities, none of it would result in any substantial increase in the wage of fast food workers because that's nominal value wages and not real value wages and any increase in real value wage is largely through the creation of better jobs, i.e. jobs that actually merit better pay because they require higher skill sets or entail gaining higher skill sets on the job (something that's never going to happen for line and counter workers in a fast food restaurant).
There's no push for substantial increase in minimum wage under Keynesian economic policies. Although the increase of minimum wage to keep up with inflation/COLA generally coincides under such policies, that's a far cry from the net increase of 107% for the past four years that some fast food workers are advocating. (Washington State ties its minimum wage increases to COLA and it's currently $9.19 per hour.)
Of course all this money has to come from somewhere which is why Keynesian economics is often associated with deficit spending. If the policies work, that can be minimized by increases in employment and real wages which in turn can result in increases in GDP and federal revenues. Regarding inflation that's dealt with by cyclically slowing down the economy which can be brought about by tax increases and increases in interest rates.
