If by the US and Canada you mean the executive branches of each country's federal governments, you might well be correct. In practice, though, you're going to end up with vocal and serious opposition whether its a Canadian province applying for statehood or a US state that wants to become a province.
On the Canadian side of things, adding an additional province would certainly require amending the constitution. Theoretically, the Supreme Court has set out mechanisms for making such an amendment, but in practice actually passing an amendment using those methods is nearly impossible. It's simply too difficult to actually get the provinces to consent. One of the first and most intractable issues that the process would run into is the senate. Canada's senate is divided to ensure regional representation. The Maritimes, Ontario, Quebec and Western Canada each get 24 senators, the territories each get 1, and Newfoundland gets 6. This arrangement has caused plenty of opposition and complaints, particularly from Alberta, because it gives Atlantic Canada a disproportionate share of senators for its population. Nova Scotia and New Brunswick each get 10 senators, the four western provinces get only 6 each.
Now, any new province is going to require new senate seats to be added, because the provinces will outright refuse to give any of their own up (as the Maritimes did when Newfoundland joined). That wouldn't be a problem on its own, but Western Canada will probably take the opportunity to demand a greater share of representation at the same time. If they do, this will be opposed by the Maritimes, and the usual gridlock that occurs whenever there's a proposal to amend Canada's constitution will set in. There are other reasons why one or more provinces might oppose adding a new province, but the senate issue is one of the most obvious.
As others have pointed out, the American senate is also a potential complication if things are going the other way. New senators for the new Canadian states will dilute the voting power that each state currently possesses. Equally relevant, any Canadian province that becomes a state, even conservative by Canadian standards Alberta, will not be putting Republicans into those senate seats for a long time. Unless the acquisition of Canadian states breaks up the two-party American political system, Republican-leaning states may object to an expansion of America that will give the Democrats more votes and more representation. There will also be issues in the US with allowing a (primarily white) Canadian province to instantly or rapidly achieve statehood while continuing to deny statehood to Puerto Rico. Valid or not, the accusations of racism would be almost inevitable.
If the political issues become too difficult to handle, dealing with another sovereign North American country might seem simple in comparison.