Congress and the executive agree to approach problems via legislation all the time - that's what's happening here.
The issue seems to be that this is an international agreement, but I'm not aware of any constitutional problem with extending normal legislation to govern international interactions, and the federal courts have agreed.
These agreements have been how every trade deal since 1890 has been implemented, and there haven't been any successful challenges on constitutional grounds. I'm not a constitutional scholar but here's Ed Meese and the Heritage foundation explaining why in their view TPA is constitutional:
http://www.freerepublic.com/focus/f-news/3301189/posts
Here's another analysis giving some good history of these agreements:
The constitution does not allow the federal government to approach such problems by being creative.
If trade is not a treaty, then trade belongs to the states.
Since, we know the states could not do trade agreements, they must fall under one of the enumerated powers.
The federal government does not get to invent powers.
The courts have been wrong on this, like they have been on so many issues in the past.
The mere fact that they want to make it easier to pass a trade bill than to kill it should be all you need to know this is subversive to the process.