Congress absolutely has a lot of power over things. Congress controls the budget and legislative direction for the country. With the passage of a law, it can shut down entire departments. With the inability to pass say, a budget, entire arms of the government shut down.

The President also has a fair amount of power too, over seat appointments, usage of Executive Orders, and one we haven't seen since President Andrew Jackson, the ability to willfully ignore things that the President is suppose to do (President Jackson famously ignored the outcome of Worcester v. Georgia to the peril of the Cherokee)