Answer:
The branch of the US government that has the power to "lay and collect taxes" is:
the Congress, according to Article I, Section 8.
Step-by-step explanation:
The Congress is made up of the people's elected representatives. As such, people's consent and approval are always sought and given through the Congress for the laying and collection of taxes. The IRS is a creation of Congress. Congress empowers it to collect taxes. Even when the Executive branch proposes tax changes, they are subject to the approval of the Congress.