To push through something can mean to succeed in getting a proposal accepted despite opposition. To push through can also mean to force something through another object or mass. The phrasal verb 'push through' can also be used to encourage someone to work through achieve something despite difficulties or pain.

1. The Prime Minister is determined to push the bill through Parliament.
2. If you are injured, it is wise to rest rather than attempting to push through the pain in order to exercise.
3. The shopping centre was so busy I had to push through a huge group of people just to pay for my shopping.

1. We can't let the setbacks we've experienced stop us from completing the task. We've got to just keep pushing through.
2. The boss pushed through the changes she wanted implemented despite clear opposition from her staff. 
3. We're trying everything we can to push the deal through before the deadline passes.