Raising the minimum wage would help a lot of Americans. It would raise wages for 35 million workers, bring 4.5 million people out of poverty, and reduce the wage gaps that plague women and people of color.
These "conservatives" are the businesses that claim to provide jobs, and who need tax breaks and lots of other help. If the poorer workers have a living wage, they can spend it on many products and services provided by many other people, including smaller companies and individuals offering their services at reasonable rates. Notice the "conservatives" rarely want to conserve decent jobs, family life and environmental values for everyone else not in their gated communities and glamorous penthouses.
Putting more money into the economy, it stimulates business