What's in it for them

The biggest driver for most TPP participants was access to the valuable US market; America's GDP accounts for 69% of the combined GDP of the 12-member bloc, Rajiv Biswas, IHS Global Insight's Asia-Pacific chief economist, told CNN in an email.

Dairy, meat and agricultural products -- especially in New Zealand and Australia -- could have made their way to the US.

Japan, the next biggest market, would drop some of its protections on domestic meat and rice, which would be a boon for foreign exporters but may hurt domestic producers.

But it would also get access to new markets for its own products -- notably automobiles.

"A number of Asian TPP signatories were expected to derive significant economic gains from the TPP and the final decision by President Trump to withdraw from TPP is a blow to their trade liberalization plan," Biswas said.

Reactions

The countries that have responded have vowed to either try to revive the TPP or enact new agreements.

Australia: "The TPP, including the United States, certainly can't go forward unless the United States wants to change its mind ... We have an agreement that has made a lot of very big gains. Gains that Australia, Japan, Canada, Mexico and other countries want to keep hold of. Which is why a number of us had a conversation about a possible TPP 12 minus one."

-- Steven Ciobo, Australia's Trade Minister

Canada: "The agreement cannot enter into force without the United States."

-- Kristine Racicot, spokeswoman for Global Affairs Canada

Chile: "We are interested in continuing the advancement of integration with countries in the Asia Pacific region, many of who were part of the TPP ... We are going to persist in the way of the integration and opening to the world."

-- Heraldo Munoz, Chile's Foreign Minister

Japan: "I believe President Trump understands the importance of free and fair trade, so I'd like to pursue his understanding on the strategic and economic importance of the TPP agreement tenaciously. The new rules that finalized in the TPP agreement after several years of negotiation will serve the model for future trade negotiations and are expected to become the 21st century global standard."

-- Japan Prime Minister Shinzo Abe, speaking to parliament Tuesday

Malaysia: "Should the TPPA (Trans-Pacific Partnership agreement) fail to enter into force, it will be a missed opportunity for Malaysia since a number of research houses have singled us out as a clear winner in the TPPA ... Should the TPPA fail to materialise, our focus would be to enhance the economic integration of ASEAN.

"Notwithstanding the current position of the new US Administration on TPPA, we will continue to engage with our American colleagues to strengthen our bilateral trade and economic relations, given the US' importance as our third largest trading partner and a major source of investment."

-- Dato' Sri Mustapa Mohamed, Malaysia's Minister of International Trade and Industry

Mexico: "Our priority is to consolidate ourselves as a relevant actor to intensify the flows of commerce, investment and tourism. And particularly before the evident difficulty due to the materialization of the TPP. Mexico will immediately initiate conversations to generate new bilateral trade accords with the participant countries in this partnership."

-- Mexican President Enrique Pena Nieto

New Zealand: "The US position is disappointing but not unexpected as the President Trump's views have been clear for some time. Our preference was to have the US involved in the TPP. However, the agreement still has value as an FTA with the other countries involved."

-- Todd McClay, New Zealand's Trade Minister

Singapore: "The US has indicated that it will pull out of the TPP agreement. Without the participation of the US, the TPP agreement as signed cannot come into effect. There are other regional integration initiatives still ongoing, including the Regional Comprehensive Economic Partnership and the proposal for a Free Trade Area of the Asia-Pacific. Singapore will continue to participate in these initiatives."

-- Spokesperson, Singapore's Ministry of Trade and Industry

Vietnam: "Vietnam considers its participation in the TPP and other FTAs​​ one further step to implement its policy of proactively facilitating the comprehensive economic integration ... which will help create a new momentum for development, and contribute to the regional integration and economic linkage. Therefore, Vietnam will continue its reforming process and make better domestic preparation to fulfill the commitments of trade agreements of which Vietnam has been and will be a member."

-- Le Hai Binh, Vietnam's Ministry of Foreign Affairs

Peru: "Obviously it is not the Trump Pacific Partnership because he has always said that he is against free trade. I am in favour of free trade because it benefits Peru ... We should work with China, the countries of Asia, India, Australia, New Zealand ... And we will make the APEC Pacific group extend to India ... We are going to take the best things of the TPP, get them in there and get the things that are not so good out of TPP."

-- Peruvian President, Pedro Pablo Kuczynski

CNN is waiting for Brunei to respond.

The rules of the game

Trade liberalization would have made it easier for manufacturers to sell goods abroad and given domestic markets greater access to foreign goods, saving each country billions in tariffs and duties.

Opponents of the deal, especially in the United States, argue that if demand for domestic goods decreases, jobs would have been sent abroad.

Though free trade and tariff reduction was a big focus of the TPP, it also set out rules amongst participants on a host of economic industries, including forced labor, environmental laws and intellectual property rights, among others.

"Its explicit aim to establish a trans-regional platform that bridges Asia and North and South America," Solís writes. "It gives its rules and standards the opportunity to disseminate far and wide."

It's not a zero-sum game, but if you're not at the table, you're on the menu.

So by being one of the TPP's first signatories, countries could help influence the rules, rather than be bound by them later on.

So is it dead?

In its current form, likely yes.

Despite the comments from TPP leaders eager to revive the agreement in some form, it won't have the heft of the original.

"While the other 11 TPP members could create a parallel agreement without the US and move forward, the economic benefits will be significantly reduced without the US participating," Biswas said.

"If the other 11 TPP members do decide to move ahead with TPP, it is possible that other Asia-Pacific countries could eventually join the TPP agreement, adding to its importance," he added.

From a technical perspective, it's nearly impossible to revive the TPP.

That means that the US and Japan would both have to ratify the TPP in its current form for it to go into effect.

The other TPP countries could in theory go back to the drawing board and amend the agreement, starting with Article 30.5.

It wouldn't be the TPP per se, but it would be similar.