People say the president has the power to set the agenda, and it's true. But presidents only set agendas they think Congress might pass, or at least consider. The president leads — but only where he thinks Congress will follow.
It's Congress that writes bills and Congress that passes them. It's Congress that can spend money and declare war. Congress, with a sufficient majority, could govern aggressively without the president's cooperation — they simply need to overturn his vetoes.
Conversely, there's little the president can do without congressional cooperation. When the president proposes an agenda that Congress refuses to consider then, like the tree in the forest, no one really cares whether it makes a sound. Anyone remember the health-reform plan that was the centerpiece of President George W. Bush's 2006 State of the Union?
The media tends to obscure this fact. We cover American politics like an episode of the West Wing — the main character is the president and everyone else is, at best, a supporting player. That's how you get bills like "Obamacare."