Clinton is trying to avoid the trade issues both because of her husband's involvement in setting up the increasingly infamous WTO, as well as a similar situation with NAFTA. (see page 9 at this Harvard link especially)
Warren is right about trade deals being able to force the changing of US laws. two cases in point are WTO-GATS forcing the 1999 repeal of the 1933 Glass-Steagall Act, leading to the 2008 world financial crisis, one of the biggest financial disasters ever, and US healthcare's crippling by GATS which has led to huge numbers of deaths in the US due to ideologically based decisions in health care which clearly were made with full knowledge that they would not work.
And these problems with WTO and GATS have created an epidemic of lying about important things by politicians. Which began in 1994, before WTO's official start.
Both 1994 healthcare "debate" was a diversion while WTO-GATS quietly started a process which effectively started a scheme to - globally- not just in the US - end the ability of countries (especially our own) to have public affordable health care using multiple interlocking "trojan Horse Clauses" like "standstill", "ratchet" clauses - and "indirect expropriation". Read much more about that in this IJHS paper and also in this 2006 document from Maine's Citizens Trade Policy Committee. (which also mentions TISA negotiations (almost finished in Geneva after nine years as possibly an even bigger threat to affordability).
The TISA and TTIP will block any government help to the poor - framing things like means tested subsidies as stealing low end customers from foreign or Third World low actuarial value insurers. Another neoliberalism friendly form of insurance may be suspended animation for the incurably ill. In short, GATS, TISA and their ilk deliberately repudiate as goals the compassion of the 20th century - replacing it with neoliberalism. They give corporations property/ownership rights to deny care to those aying less framing that as the natural order of things - anything else is trade distorting- They give corporations permanent - as in forever- ownership rights to remain in and control our market which are superior to our interests. The mere presence of a health insurance industry becomes carved in stone and governments are forbidden from doing anything whatsoever which adversely effects their profits - Its unambiguous that most of the positive parts of the ACA would be struck down (rolled back to 1998's levels of "market liberalisation") prevents single payer and makes any public health care unsustainable because of the need to charge more money and coddle commercial firms and also that is prohibited by GATS two part test in Article 1:3. So doing anything competes with any commercial offering (not just health care, also schools, water, housing, and hundreds of other essentials will be prohibited to governments.
TISA and TTIP - and GATS - will destroy our futures- Most importantly, we absolutely cannot let any foreign insurers into the country or our cost to extricate ourselves from GATS will increases a thousand fold. Also both TISA and GATS are putting us on a path to lose many formerly public sector jobs due to "services liberalization's" "fourth mode of supply". Basically, global temping for low wages. This would give an intenational entity like the WTO the ability to compel the US to eliminate any policy it saw as a trade barrier like minimum wage or restrictions on visas or licensing which excluded otherwise qualified foreign firms which had been low bidders. Also, there would be a standstill on new laws which restricted the making of profit (such as minimum wage or environmental regulations) People should read the summary of the TISA talks here and consult the papers it references - and a trade glossary for the meaning of these terms. Can the WTO, once a service sector becomes globalized (and falls under their jurisdiction), declare a minimum wage or some other rule, like a visa quota, or licensing requirement, to be a technical barrier to trade- a trade or market entry barrier? It did exactly that with El Salvador in the 1990s, compelling the nation lower its minimum wage from 60 to I think 36 or 38 cents an hour or face trade sanctions.