Well, then they require 2/3 approval in the Senate.
Of interest:
http://constitution.findlaw.com/article2/annotation12.html
... The Constitutionality of Trade Agreements
In Field v. Clark, this type of legislation was sustained against the objection that it attempted an unconstitutional delegation ‘’of both legislative and treaty-making powers.’’
The Court met the first objection with an extensive review of similar legislation from the inauguration of government under the Constitution.
The second objection it met with a curt rejection: ‘’What has been said is equally applicable to the objection that the third section of the act invests the President with treaty-making power. The Court is of opinion that the third section of the act of October 1, 1890, is not liable to the objection that it transfers legislative and treaty-making power to the President.’’
Although two Justices disagreed, the question has never been revived...
Because the Senate is the only body with standing to challenge a "trade agreement" as being in violation of the Treaty clause. And the Senate no longer wants this power.
Ted Cruz, as a member of the Senate, could mount a campaign to restore the Treaty authorization clause of the constitution, but instead he signed on the TPA, which removes even the power of the cloture to stop a bad treaty "trade agreement."