It's not that simple. While it is true that government workers are part of the economy and in return pay their share of taxes, there's a big difference between them and private sector. The private sector generates money, the government absorbs that created wealth that the private sector had to create. The larger you make the government sector, the smaller the private sector gets. In turn, not enough wealth to support government.
Life is hard, there's not always an easy solution. Can't just throw government at every challenge in life. Notice there's constant proposals for every challenge. Health care, college education, child care. People want government to pay for everything that is expensive and they don't think they should be responsible for.