Traveling to Canada as a US Citizen for a very short trip

Canada would require proof of U.S. citizenship, which a birth certificate may or may not suffice.

But U.S. law requires that U.S. citizens enter and exit the U.S. with a U.S. passport except as provided by the President. And what the President provides is what the CBP requires, documented here. Basically, a passport, passport card, Enhanced driver's license, Global Entry/NEXUS/etc. card, or, if you are under 16, just a birth certificate. I don't know if your driver's license is an enhanced driver's license, but if not, you can get one (if you're in one of the states that offer it), or get a passport card or one of the other types of frequent traveler cards.

To enter into Canada you need http://www.cbsa-asfc.gc.ca/security-securite/admiss-eng.html

If you are a citizen of the United States, you do not need a passport to enter Canada. However, you should carry proof of your citizenship, such as a birth certificate, certificate of citizenship or naturalization, as well as photo identification.

(this contradicts the other answer saying "Canada would require proof of U.S. citizenship, which a birth certificate may or may not suffice" -- it will suffice.)

To enter into the USA by land http://www.cbp.gov/travel/us-citizens/whti-program-background/docs-land-sea

U.S. citizens and nonimmigrant aliens from Canada entering the United States by land or sea are required to present a valid WHTI-compliant document, which include:

• Passports
• U.S. Passport Cards
• Enhanced Driver's Licenses
• Trusted Traveler Cards (NEXUS, SENTRI, Global Entry or FAST)
• Military Identification Cards (for members of the U.S. armed forces on official orders)
• U.S. Merchant Mariner Document (for U.S. citizens on official maritime business)
• Enhanced Tribal Card (where available)

Therefore, if you have "birth certificate, driver's license" and that's an "enhanced driver's license" (EDL) then you are good for both countries. You can study https://help.cbp.gov/app/answers/detail/a_id/1269/~/what-is-an-enhanced-drivers-license-(edl)%3F this page about the EDL.

While this is the official version, the reality is that US citizens can always return to the US if they can convince the border officer that they are indeed citizens (this is indeed the case for every country for their own citizens, this is an essential part of being a citizen). This is murky and can get complicated.