Isn't it a main responsibility of POTUS to lead and manage the legislative branch?
Well, no, it's not. The primary function of the POTUS is to be the chief executive of the administration. That is, all the agencies, administrations and departments of the federal government. So, along with that comes the responsibility to make appointments to the various non-legislative parts of the government... the dept of justice, for example. So it also goes with firing the other executives in federal government.
The influence of the POTUS on congress is really very small. He can offer vision or direction to the congress from the standpoint of what laws he says he will sign or veto, and the POTUS is going to lay out his direction every year in the state of the union address, but he has no vote in the making of legislation, no leadership role on any committee, and no legislative responsibilities other than the enacting or vetoing legislation at the end. There is a little niggle in that the president can convene or adjourn congress on the occasion of sweeping national tragedy, attack or martial law, but those are true rarities. The VP is the president of the senate, and that means he can cast tie-breaking votes in the event they are needed, but even this is a very limited role in the congress. One would suppose that the VP, if casting such a senate vote, would reflect the position of the administration and by extension the chief executive, but that's not written anywhere. In the early days of the country, the vice president was the guy who came in second in the presidential race, and had opposing views.
There's also the POTUS role of commander-in-chief of the armed forces, which he has for practical decision-making. We have the joint chiefs, but ultimately it's the president that is the one with the responsibility for what they do.
The POTUS is the single highest representative of the nation in foreign policy, and as he holds the top position over the secretary of state, he's responsible, ultimately, for making treaties with foreign nations.
That said, at the minimum, his rubber stamping of extending the Patriot Act perfectly demonstrates how his actions differ from his campaign platform and his ability or need to stand up for the people that elected him.
Well, anyone can hazard a guess, but I think history will probably treat him better than you think it will, though I do agree that he hasn't lived up to expectations. I'll also add that expectations were set uncommonly high. Between the time he got elected and when he took the oath, he was given a pretty cold and deep soak in the dirty bathwater from the previous administration -- and by that I mean extensive debriefing by the leaders of all the various departments of the government in the outgoing administration. Anyone with half a brain would change their opinions when presented with the real-life playbook left my the former tenant of the white house. I have no doubt that the national security stuff in particular was especially hard for him to change course on, as it wasn't part of his set of strengths. We were also at war in 2 places at once and he didn't want to be in any more of those, so he was pretty hawkish about looking out for threats.
Anyhow, I'll close with the observation that many people missed about him from the start. He was, and is, very much a person who wants consensus. He was far far too willing to kowtow to the demands of people that wanted him to leave the status quo in place -- and here I'm talking about the neocon chickenhawks and the big wall street banks. He did not, as most presidents do, clean house at the justice department and remove all the bush-era appointees, for example, even though they all got their JDs from Oral Roberts U and Liberty U and were diametrically opposed to everything he wanted to see. He let them stay, as a conciliatory gesture, hoping that it would earn him a place at the table with his nominal opposition. What he took awhile to learn is that he could not make nice with these people. They would never accept partnership with him. They would not work to higher goals if it meant having any kind of agreement with him. We saw it in congress, especially. So here's a guy who really did want to make things work and was ready to give a little on a few things to show he could be a good partner, but what he gave his opposition they ended up taking and running away. I can only point to the tone he began to set in the days just after this most recent midterm election, which was much more strident and decisive than anything he'd said previously.
So, while you will say he's bound to be seen as a flash in the pan, he is the president we had in the second most damaging collapse in the world economy in 80 years, he was the only president to enter office while 2 simultaneous foreign wars were in full-swing, he was the only president to be able to change a health care system that was basically unreachable for almost a quarter of the nations people, and he's made very real progress in world diplomacy in areas that the nation hasn't ever touched before -- Iran and Cuba, mostly. Sure, he's a polarizing figure, too. If he were a flash in the pan, nobody would notice and nobody would care.
No, he's not perfect, and there's a lot I was hoping he'd do that he has not (getting rid of the TSA, undoing the bloated bureaucracy of the DHS, closing GITMO, retiring the Patriot act, dampening the NSA powers, etc.) but I think it's been pretty good on balance and he'll get a fair treatment by the history books.