Does the US govt spends more on health care than Canada's govt?

Yes. Both in absolute terms and per capita the US spends more on Medicare, Medicaid, and other health programs than all of Canada spends on its health care. This provides care (or partial care) for about 25% of Americans. Another 20% have no care. The other 65% pay for private insurance.

However... it would be a mistake to assume that prices go down merely because you have a government insurance option or even government only insurance. Canada's health care is also significantly cheaper to deliver for a wide variety of reasons -- legal systems (loser-pays civil systems, caps of damages, etc.), lower insurance costs, pre-negotiated fees with doctors, less administration (governments own the same hospitals), no advertising (hospitals aren't competing with each other, drug companies aren't selling to different hospitals), higher utilization of equipment (government buys MRIs based on need rather than every hospital having one), centralized billing systems (single-payer system, ), better education systems (sex education in school, PE requirements, health and fitness education, etc.), lower patent times on prescription drugs, no illegal immigration, lower violent crime rates, lower hard-core drug usage rates, firearm laws, government supported preventative care (mammograms, subsidized athletics programs for people, etc.), able to use less costly care options (home support, community nursing, prenatal classes, etc.), lower STD rates, lower teen pregnancy rates, lower obesity rates, etc., etc.

Americans spend more because more don't have any health insurance.

Government care will increase the rates.