If I were living in the United States, I would have really hard time deciding whether I'm a "liberal" or a "conservative". (I understand that there are other options as well, the so called "independent" parties, but in practice supporting them is rather inconsequential because the United States is a heavily, heavily bipartite system, with only two real choices that matter. The third option is effectively, for all intents and purposes, the same thing as not voting at all.)
Sometimes it's actually hard to know what the exact differences are between liberalism and conservatism (at least when talking about American politics). There are quite many things that one would ascribe to liberalism which a conservative would most probably say "we support that too!"
Well, Google is a great tool for this too, and after some quick research, here are a few things that demonstrate that I couldn't in good conscience subscribe solely to either political position. (Note that these are just averages, rather than describing every single individual person in either camp. In other words, a good majority of people in those camps subscribe to these, but not necessarily all of them; and there are probably degrees of acceptance.)
In the question of affirmative action, liberals are in general for (probably with exceptions), while conservatives are in general strongly against. Well, personally I am likewise strongly against it, because I'm an individualist (ie. I believe treating people as individuals, not as members of artificial groups, giving every individual person the same rights regardless of inconsequential superficial characteristics) rather than a collectivist, and I strongly think that affirmative action is sexism and racism in its purest form, and an affront to individual human rights. It's also quite unambiguously illegal and unconstitutional in the United States. I suppose that would make me an ultraconservative in this regard (although I think many "liberals" would agree with me on this as well.)
In the question of death penalty I'm slightly ambivalent, but leaning towards being against it. With this I'm not saying that I support the death penalty; rather, I'm saying that this is not necessarily a clear-cut black-and-white question, and that arguments should be listened and not just rejected outright by putting one's fingers in one's ears and shouting "lalala I can't hear you!" But if I were forced to choose either option, I would definitively choose to be against it. I suppose that would make me fall on the liberal camp.
The question of economy is a difficult one, because I recognize that I am not an economist and I have basically zero education on the subject, and thus anything I say will be pure speculation. But I would fall somewhere in the middle of the spectrum: I think capitalism is the form of economy that works best in our society, the form that best drives innovation, progress and well-being. No other economic system seems to work as well. However, I also think that it should be heavily regulated by a strong government, to stop abuses by big corporations. The rights of the consumers are of paramount importance, and the power of big corporations over individual citizens must be controlled and scrutinized, and abuse must be penalized and stopped. That being said, markets should nevertheless be mostly free, rather than government-owned or controlled. (In other words, the government should regulate fairness when dealing with citizens to stop abuse of power, but in terms of economy, a free market is the best option.)
Living in Finland, where the schooling system is one of the best in the entire world, I know that a good public school system, and the abolition of private schools, is the best option. This is not just hypothetical wishful thinking; it's actual concrete real-life proof. Thus my choice is pretty clear. The liberal side wins hands down on this front. Thinking anything else would be denying reality.
Likewise Finland has one of the best public healthcare and social security systems in the world, and it works. Actual concrete proof, rather than utopistic hypotheticals. So, once again, the liberal side wins hands down.
In the question of immigration, however, I have to swing to pretty much the other extreme. I just have to take the ultra-conservative stance here: There is, generally speaking, a reason why immigration is heavily, heavily regulated and restricted. It's not just a question of nationalism or xenophobia. It's a question of pragmatism. Mass immigration with little to no limits is destructive to the hosting country. That's just how it is. Again, thinking anything else is just denying reality (which so many liberals are so fond of.) There is a reason why immigration laws are in place, and they should be followed. Strict immigration laws are necessary for the country to keep functioning properly. That's just how it is. One country cannot be the savior of the world, no matter how much suffering there is out there. Just bringing that suffering into the country en masse is not going to fix it; the only thing it's going to do is to destroy that country. In fact, if a country wants to help other countries, it's economically much more efficient to bring the help to them, in situ, rather than bringing all those people here. That's not going to fix any of the problems there, and it's only going to cause problems here; it's a lose-lose situation, and it just doesn't work. As harsh as it may be to say, immigration should benefit the hosting country; charity does not help neither. (Some charity can be done, but only within reasonable limits.)
In the question of taxes, I have to once again sit in the middle. Some taxation is necessary for the society to work, for the public schools, public healthcare and social security to work. On the other hand, over-taxation of companies and rich people only stifles the economy and drives them away from the country, and that's not healthy. There has to be a balance. Not too much, not too little. The proper amount.
The United Nations is also a point of contention between liberals and conservatives. I think that the UN is mostly a joke. They might have done some good things, but they are also laughably incompetent, biased and crooked in others. The good things don't justify the bad ones. It's a heavily politically corrupt organization, with heavy unjustified biases. I don't know if the world would be a better or worse place without the UN, but it would be once again denial of reality to think that it's not a completely corrupt, biased, incompetent and inefficient organization. But perhaps it's a necessary evil, and the world would be worse without it; who knows.
The liberalism vs. conservatism question is becoming ever more so complicated in recent years, due to the antics of the "regressive left" movement, which is a highly authoritarian in-name-only left-wing liberal movement of "social justice" and "feminism", which is giving liberalism a bad reputation. It engages in all kinds of authoritarian, even totalitarian, ideologies and practices, which is completely contrary to liberal ideas, and is destroying the reputation of liberalism.
As a concrete example, there's now on Twitter an all-liberal committee of people who decide who should and shouldn't be banned, and they shadow-ban people who have particular views, specifically conservatives. This is a complete affront to the core principles of liberalism and basic human rights: Biased banning and censoring opposing political views. This is totalitarianism, and one of the hallmarks of fascism. And it's being done in the name of liberalism.
And that's just one example of many. Conservative extremists in the United States are, in fact, using these examples to attack and ridicule liberalism. Telling to them that that's not what liberalism is about, and that they are not, in fact, liberals but pretty much the exact opposite, falls to deaf ears. Conservatives are using these totalitarian fanatics as a weapon against liberalism.