"Public backing" means having the support or approval of the general public for a certain idea, action, or cause. It shows that the majority of people agree with or believe in something. Full definition
If the government is acting confidently, it is because it knows it has significant public backing for its welfare reforms plans. (politics.co.uk)
However, the proposal has not received any significant public backing. (sputniknews.com)
In response to the disruptions and increased public backing of the farmers, a number of processors increased the price they pay to dairy farmers for raw milk. (dairyreporter.com)