Strictly speaking, the president doesn't make laws. Although presidents are involved in the process, they are not members of the legislative branch, but the executive. They aren't some super-PM. The reason why the president is involved in the process is a part of the system of checks and balances. Generally speaking, Congress makes laws, the (federal) judiciary interprets them, and the executive enforces them. The president has gained powers over the centuries, but they don't make laws.
The reason why the Supreme Court is currently swung to the right is because we've had a pretty good run of conservative presidents since 1980. The president appoints the Supremes. The Senate confirms. After that, they are in until they retire, die, or are removed. They are meant to be non-political, so no democratic vote other than people electing the right president, and to a lesser extent, the right senators and representatives. This is why I mentioned Supreme Court nominations as a vital reason why we needed to re-elect Obama, if not the most vital. The nominations a president makes can last decades. We still have two Reagan appointees.
The reason why DOMA may be overturned is because marriage crap is usually left to the states (10th Amendment). That would be a bad way to overturn it (at least in my limited understanding) because it would allow states to continue to ban same sex marriage. It would also mean that those who are married in states that allow same sex marriage or civil unions have little security in their legal status. Not that they do now, but since it had been heard by the Supreme Court, it could take a while to have another case heard by a (hopefully) more progressive court.
If they strike DOMA AND California's ban, it would be something akin to the case
that brought interracial marriage bans to an end. I'd be shocked if that happened because of the make up of the court, but stranger things have happened. That is why most supporters of gay marriage were hoping to hold off until someone retired or popped their clogs. Unfortunately, it may be Kennedy (who is a moderate sort of libertarian sort of guy who does the swing vote) or Ginsburg (left of the court). I guess it would be better to replace them before a Republican gets in, but I'd love to see Scalia and Thomas out of there as well.
ETA: A good explanation of why the Supremes are appointed, not elected is they are meant to make decisions based on case law and the constitution, not what is going to make them get re-elected. Can you imagine what would happen if they heard a case where a death row inmate was not given his or her protections under the law yet to grant a reprieve would mean a justice might lose re-election? Sometimes this leads to a court whose views are behind the times in relation to what the general American population feels, which might happen with same sex marriage, but it can also protect the rights of the minority against populist will.
Direct democracy doesn't always translate to even handed justice.