Due to Child Support arrearages, I cannot get a passport. This is preventing me from travelling abroad in the Philippines. She can get to Canada - I can get to Canada - but how do I return if they require a passport?
This is what the law says (8 USC 1185(b), also known as INA 215(b)):
Except as otherwise provided by the President and subject to such limitations and exceptions as the President may authorize and prescribe, it shall be unlawful for any citizen of the United States to depart from or enter, or attempt to depart from or enter, the United States unless he bears a valid United States passport.
However, there are no known penalties for violating this law. In fact, I would say that this law is routinely violated, by some dual nationals who leave the U.S. without a U.S. passport, on only their other passport (which is trivial since there are no exit checks), due to ignorance of this law, or due to the false misconception that not getting a U.S. passport allows them to not be a U.S. citizen.
The "exceptions" that the President authorizes are summarized in this CBP answer. Basically, for land crossing, other than for children, you are supposed to have a passport, passport card, enhanced driver's license, or a card from one of the trusted traveler programs.
If they won't give you a passport, I doubt they will let you in one of the trusted traveler programs. The enhanced driver's license is only available in some states; e.g. if you still live in California then you cannot get it. So it is possible that you won't get any of the documents on that list.
So then your question is: Can I enter the U.S. from Canada with no passport or other appropriate document as a U.S. citizen?
The answer is Yes. Although it is "unlawful" for you to enter, that does not mean they can deny you entry. They can refuse to issue you a U.S. passport. But if you manage to arrive at a U.S. border, they cannot deny you entry under any circumstances, as long as it is satisfactorily established that you are a U.S. citizen.
You need some proof of U.S. citizenship, like an old U.S. passport, or a U.S. birth certificate, Certificate of Naturalization, Certificate of Citizenship, Consular Report of Birth Abroad, etc. (the same evidence you would need to apply for a passport). Since you were born in the U.S., you would use an old U.S. passport or your birth certificate. Birth certificate will likely cause more scrutiny since it's easier to fake or fraudulently use those, and it doesn't have a photo so you should use it with another photo ID.
Here are some relevant parts from the CBP Inspector's Field Manual (IFM) (the Customs and Border Protection released this publicly a few years ago and many immigration websites have copies of it; I have heard that CBP has switched to a different manual last year, but it is still informative):
When you are convinced that an applicant for admission is a citizen of the United States, the examination is terminated. [...]
Consequently, the examination of a person claiming to be a United States citizen is limited to matters required to establish present citizenship. Once you are satisfied the person being examined is a U.S. citizen and any required lookout query has been completed, the examination is over.
When an applicant fails to present a passport or presents an expired document, the immigration officer shall, if satisfied that the person is a United States citizen, advise the individual of the necessity of having a valid U.S. passport. Although technically you are waiving the passport requirement for the Department of State, no form need be completed. In addition, there is no fee collected by INS.
So basically, if you fail to present a valid passport, they will "advise" you about the benefits of having a passport (which you can't get anyway). And then they will grant you a "waiver" of the passport requirement, which is a formality because neither you nor they have to do anything special, and there is no charge.
Also, just because the immigration inspection is done doesn't mean that Customs can't inspect your baggage (like they do for everyone entering). But the most they can do there is seize your stuff, they still can't prevent you from entering (unless they are arresting you for having illegal stuff).
To enter Canada, yes, it's true, you can just use birth certificate and photo ID (source)
From the Department of State's website on travel to/from Canada, for returning to the US, you'll have to do it by land.
When traveling by air from Canada, U.S. citizens are required by U.S. law to present a U.S. passport
while by land:
For entry into the United States via land and sea borders, U.S. citizens must present either a U.S. passport, passport card, NEXUS card, Enhanced Drivers License, or other Western Hemisphere Travel Initiative (WHTI)-compliant document. The only exception to this requirement is for U.S. citizens under the age of 16 (or under 19, if traveling with a school, religious, or other youth group) who need only present a birth certificate, Consular Report of Birth Abroad, or naturalization certificate.