Washington (CNN) President Barack Obama will have to wait longer to announce the biggest free trade deal in history.

Trans-Pacific Partnership negotiators wrapped up their most recent round of talks in Hawaii on Friday without reaching an agreement on what would be a 12-country pact that encompasses some 40% of the world's economy.

Together, they vowed to continue the talks -- but didn't set a date for their next round of negotiations, indicating the deal's future remains uncertain after two years of claims that its conclusion is near.

The White House had hoped that a measure Congress passed known as "trade promotion authority" would prompt other countries like Japan, Canada and Malaysia to improve their offers and seal the deal. The measure guarantees uncomplicated passage of the deal in the United States via an up-or-down vote without amendments.

But several sticking points remain.

Dairy, cars, currency

Canada is balking at opening its dairy market for more imports -- a key demand not just of the United States but also of New Zealand, where dairy giants like Fonterra are eager to expand the country's top export.

In Japan, the United States wants easier access for its agriculture and automotive companies, but Prime Minister Shinzo Abe faces a legislature strongly influenced by small rice farmers. Long-standing foreign auto trade barriers are difficult to tear down in that country.

And the United States' push for 12 years of patent protection on pharmaceutical drugs is tripping up poorer countries -- such as Malaysia and Vietnam -- that fret they'd face public health challenges without access to cheaper generics.

Critics in manufacturing states have said the deal should include a crackdown on countries that manipulate the value of their currencies to give their exports a price advantage in the United States. That, though, is a non-starter and would halt the deal's progress entirely, negotiators from several countries have said.

Democratic critics attack it

Unfinished, the Trans-Pacific Partnership is already a political flashpoint in the United States.

Obama is under the gun to get the deal done soon, if he wants it to be complete before he leaves office in January 2017. He needs to allow for months of congressional review, text scrubbing and language translations that are inevitable before a vote in Washington.

At the same time, he faces criticism from his own party's liberal base.

It's led by firebrand Massachusetts Sen. Elizabeth Warren, who has lambasted the deal's inclusion of what's known as an "investor-state dispute settlement mechanism." It would allow companies to challenge countries' laws and regulations to an international arbiter.

It has been used in other trade deals by companies like Phillip Morris International to challenge public health measures like cigarette plain packaging laws. The cigarette maker has alleged that its intellectual property -- its branding -- has been being unfairly devalued.

But the mechanism is also helpful, supporters argue, when property rights are assailed by countries involved in the deal.

Labor rules

Democratic Rep. Sandy Levin of Michigan, meanwhile, said it's "wise" that the deal wasn't concluded this week.

Labor rules with countries like Mexico, Vietnam and Malaysia still need to be better addressed, and the United States shouldn't curb access to medications, he said.

"We will also need to closely review the still-classified text to assess the extent to which there has been real and sufficient progress on issues such as the environment and investor-state dispute settlement," he said.

Hillary Clinton has echoed liberal criticisms of the deal. Republican presidential candidates, meanwhile, have largely advocated its conclusion.

Some Congressional Republicans said they're encouraged that the talks will continue.

"The negotiations have not yet reached an agreement that meets the high standards set in TPA (trade promotion authority)," House Ways and Means Chairman Paul Ryan, R-Wisconsin, said in a statement Friday night. But he supported continuing negotiations to get the best possible deal.

No time line

Trade negotiators vowed in a joint statement to continue their work, but didn't offer a time line.

U.S. Trade Representative Michael Froman and other countries' trade ministers said in a joint statement that they plan to continue the talks. They said the countries involved in the major disputes will talk one-on-one with each other.

"Ministers and negotiators leave Hawaii committed to build on the momentum of this meeting by staying in close contact as negotiators continue their intensive engagement to find common ground," the statement said.

They also vowed that the end of the negotiations is near and that they are "more confident than ever that TPP is within reach."