The Senate bill is the worst of all worlds - having citizens pick up the tab for illegals and surrendering ourselve to a foreign body (100m+ chain migration) without getting anything in return. Annexing Mexico would be a fair payment-in-kind (PIK).
As for Canada, there's no one up there. They have this huge country with less people than Calif. Who would absorb whom?
There is no 'or'. The Constution clearly authorizes controlling the border and citizenship. It does not authorize going 'whole hog on the whole pot'. To entertain any other idea, is to consider the overthrow of our government for something else.
We cannot 'annex' Mexico. We can conquer them (which would be abrogating our constitution), or we can allow Mexican citizens to vote to become a territory of the United States, then allow the states to vote on whether to let them in.