Trump is sending Treasury Secretary Steven Mnuchin and Kudlow, as well as his trade officials, U.S. Trade Representative Robert Lighthizer and Peter Navarro to China. But it's unclear what will come of those talks, intended to head off a tit-for-tat trade skirmish. The negotiations also come as China has been cooperating with the U.S. to curb North Korea's nuclear program. Those talks also come just days after the historic meeting of the leaders of North and South Korea.
"There's clearly a battle going on in Trump world between those people who understand the global economy and those who are protectionists. Larry Kudlow has a global view of the world and Mnuchin does," said Tom Block, Washington policy strategist at Fundstrat.
Block said the conflicts within the group also make it difficult to know what the exact goals or outcome could be for the China talks.
As for the TPP, Block said he doubts it has a chance of being revived for now, even though Trump said in front of an agricultural audience that he would reconsider it.
"[TPP] was envisioned to be part of a counterbalance to growing China. It made sense then. It makes sense now, but I think it's going to be a hard sell to the Trump base," said Block.
Even if Trump wanted to reconsider the TPP, there are many hurdles to the U.S. returning to it. But America may find its farmers and businesses are at a disadvantage because they are not in it.
Kim Wallace, managing director at Eurasia Group, said the member countries would find it difficult to meet Trump's demands to improve the TPP in America's favor.
"It was a missed opportunity, not only economically but geopolitically. That's part of the reason for developing and implementing trade blocs. You play really nicely with those in your sandbox, and with others not so much. When you look at growth trajectories in both terms of economics and demographics, it's been known for at least a decade that this is one region you had to have a foothold in," he said.
New Zealand, an early member of the TPP, said the U.S. cannot simply jump back into the agreement, though it would be welcome. New Zealand Prime Minister Jacinda Ardern said recently that she could see the U.S. rejoining but not without renegotiation, and that would have to be approved by all 11 countries. Other members include Canada, Australia, Mexico, Malaysia, Singapore, Chile, Vietnam, Peru and Brunei.
"Trump is correct that the TPP would be a big boost to U.S. agriculture. But we have seen this a few times and are not too optimistic on its chances of happening in the short run," said Daniel Clifton, head of policy research at Strategas Research. "Trump's real focus is on securing a bilateral trade agreement with Japan and to rebuild TPP from the bottom up rather than the top down."
The U.S. has said it would put tariffs on $50 billion in Chinese goods, and China responded by pledging to put tariffs on U.S. goods and agriculture. Trump also has threatened to up the ante by putting tariffs on another $100 billion of Chinese goods, and China says it will respond.
"The only reason the Administration even dipped their toe in these TPP waters was because it is a full-throated anti-China move. The entire strategic point of the TPP is to fortify an economic ring fence … around China," wrote Chris Krueger, policy analyst at Cowen.
The payoffs from re-engaging in the TPP could be important to the Trump administration, as it works with Asian allies on North Korea's nuclear ambitions.
"It embeds the United States in the future of Asia. It anchors us. It tethers us. It's a strong commitment in shaping the economic future of the region," said Sheila Smith, senior fellow for Japan studies at the Council on Foreign Relations.
The U.S. is tangling with China on one front and is trying to resolve the renegotiation of the North American Free Trade Agreement with Canada and Mexico before the Mexican election in July.
"Once NAFTA is done, I do think there is going to be attention paid maybe not just to Japan but to the region," said Smith. The TPP was a way to correct some of the issues that were not working or outdated in NAFTA, she added.
Domestic politics could continue to be a problem for U.S. consideration of the TPP, and there are wild cards, including how the administration prioritizes it and what Congress might demand of a deal. "If you have a change in leadership in one or both houses of Congress, they may not want a new trade deal until after the next presidential election," said Jeffrey Schott, senior fellow on international trade at Peterson Institute for International Economics.
"The other countries have demonstrated they are going forward without the U.S. There is this growing discrimination against U.S. farmers and exporters in the region," he said. "Certainly it will deepen once TPP 11 goes into force."
The road back to the TPP could be tricky, if not impossible. "Near term there's not much that can be done, because the agreement isn't in force. The prospect for session negotiations will really only become serious next year. But the other countries are unlikely to make major revisions in the existing text that was signed in March in Chile," he said.
Schott said it's not clear what Trump meant by a better deal or whether one is possible. "Bigger and better would be more countries participating, which means there would be a bigger economic payoff and that would likely occur once the agreement enters into force and other countries join. Already there's consideration in South Korea, Taiwan, Colombia and the United Kingdom, among others," he said.
Wallace said it would be a "long slog" if the U.S. tried to rejoin but it's not likely.
"The biggest downside of that is time, in my view, given what's going on in the region, and what has been going on in the last 15 years in the way of economic growth in the region," said Wallace. "It is possible the TPP countries look and say we're comfortable with our trade relationship once the U.S. figures out what relationship it wants to have."