President Donald Trump announced a new bilateral trade agreement with Mexico on Monday.

The deal would rework several trade rules dealing with cars, intellectual property, agriculture, and more.

But many experts and groups have attacked the new deal, including some long-time Trump allies.

President Donald Trump heralded a trade deal with Mexico as a new day for the North American Free Trade Agreement, but many of his top allies aren't thrilled by the agreement.

The deal announced by Trump and Mexican President Enrique Peña Nieto on Monday proposes to revise rules dealing with the treatment of automobiles moving across the border, intellectual property, and labor.

Trump called the deal "incredible" and suggested that the US could pull out of NAFTA completely and simply move ahead with the Mexican bilateral agreement instead of involving Canada in the new deal.

"So it's an incredible deal," Trump said in the Oval Office. "It's an incredible deal for both parties. Most importantly, it's an incredible deal for the workers and for the citizens of both countries."

(Read more: Here's what's in the US-Mexico trade deal »)

But for many of the president's ideological allies — from conservative think tanks to Republican lawmakers to the influential editorial boards — the sentiment appears to be that the deal is better than breaking NAFTA completely, but it's not a good deal.

Most of the critics pointed to the increased regulatory burden of the automobile rules and possible higher costs from the stronger labor protections, saying these provisions would increase government's role in the economy and prevent companies from operating efficiently.

Here's a rundown of some of the criticism: