The approval of the Senate
The Legislative branch has the power to make treaties according to the Constitution, but many Presidents use a loophole to bypass the need for legislative approval and make foreign policy with the executives of other nations called "Executive Agreements". These agreements are essentially the same as treaties.
The Executive branch decides is a treaty is unconstitutional
It isn’t a treaty nor valid.
In the United States, the Executive Branch (President) will negotiate a treaty, and it must be consented to by the Senate with a 2/3 affirmative vote. After this, the President can ratify the treaty.
The president can make executive agreements with foreign heads of state that do not carry the status of treaty and so avoid Senate confirmation.
In the United States, the Executive branch provides the process for signing and approving treaties with foreign entities (generally the responsibility of the President).However, the Legislative branch (specifically the Senate) is responsible for ratifying any treaty signed by the President. A two-thirds majority in the Senate must approve the treaty in question for it to be officially ratified.
The Executive Branch (the President/State Department)
two-thirds
In the US, the power of the executive branch of government has been growing. This impacts both foreign and domestic affairs. For example, the US president signed a executive order to create a set of policies that allows Iran to make certain limited progress in nuclear physics in return for the unfreezing of assets mandated by violating UN resolutions. The US Congress opposed this so-called treaty but did not have enough votes to overturn the treaty with Iran. In years past, a US president seldom made foreign treaties or agreements without the support of the US Congress, specifically the US Senate. Executive power may be reaching a point of critical mass however.
The executive branch (the president) has the power to with the consent and advice of the Senate.
In the United States the executive branch appointed people to negotiate treaties with Native Americans. The treaty was not in effected unless it was in line with the advice and consent of the US Senate. Certainly there may have been minor details of a treaty the the executive branch was allowed discretion.
the president can sign a treaty but congress has to ratify it in order for the US to enter into it. So I guess congress is the only branch of government.