The President also has the bully pulpit and his honeymoon period. During the honeymoon period (which typically falls right after election, excluding some cases like Bush Jr who seemed to have it right after 9/11) you can get damn near ANYTHING through congress, oftentimes even if the party in power is the other one.
And even so, unless the President has become a COMPLETE joke, or Congress has a much higher approval rating (which almost never happens) the President can pretty much call a press conference and say “the meanies in Congress aren’t passing my bill to help you, write them and tell them you’ll never cast a vote for them again unless they pass it.” And oftentimes he can still get it through with that, though this admittedly works a lot better when the majority party is that of the president. The president can, of course, also call a press conference at the same time as congress to make certain that less people know what they said, or at least not know it too soon (because the president’s conference is always the one focused on), though that’s a bit circular, the media focuses on him because of his power, he has power because the media focuses on him.
Not to mention the President appoints judges, who are the REAL powerhouses, yes, Senate confirms, but that’s still a pretty big power - considering the fact that I’d argue the judicial branch is the most powerful branch of the government (hell, you could argue they were since Marbury v Madison established judicial review, they’ve only gotten more powerful since then).
Add that with what the posts above said about the Senate being only elected by local bodies.