The phrase "push for action" is correct and can be used in written English.
It means to strongly advocate or encourage for something to be done. Example: The community leaders are continuously pushing for action on the issue of gun control.
| Fed officials push for action to support the economy.
Corporate giants Mars, Walmart and Citi are expected to push for action on climate change.
But a small yet growing number of Republicans, conservatives, and libertarians are starting to push for action on climate.
It is also, for her, a motivation to continue to examine these issues and to push for action through her bilingual Web site, Destiny's Children.
Weinstein's wife and two daughters made a new push for action, now in the context that the US would and had negotiated a prisoner swap.
Immigration has taken a backseat to other issues lately, but there has been a renewed push for action in the House of Representatives.
As you point out, the continuing disaster in the Gulf of Mexico provides a rallying point for President Obama to push for action on climate and energy legislation.
Mr. Cuomo, in turn, declared his support for bringing diversity to state government and promised to push for action to combat joblessness among minority youths.
This push for action against climate change is supported by the London Organising Committee of the Olympic and Paralympic Games (LOCOG).
Senator Tom Daschle, Democrat of South Dakota, has said he will use his new power as majority leader to push for action.
Samantha Power, President Barack Obama's nominee to be the US ambassador to the United Nations, has promised to push for action on Syria during her Senate confirmation hearing.
