From Longman Dictionary of Contemporary Englishbalancing actˈbalancing ˌact noun [countable usually singular] when you are trying to please two or more people or groups who all want different things, or who have ideas that are completely different from each other Gilmore had to perform the difficult balancing act of attracting moderate voters without losing his Conservative base.
Examples from the Corpus
balancing act• The question now facing voters is which approach is likely to achieve the best balancing act.• Richard was engaged on what must often have appeared to him to be a bewildering balancing act.• But it's a crucial balancing act where you have to prioritise on a daily basis.• It was a tricky little balancing act.• Now that balancing act has become more precarious than ever.• Neither half of that balancing act has yet met with success.• Using political power to reduce market inequalities requires a high-wire balancing act. 