The assembly, which is made up of a network of 57 civic organisations, said it was likely to petition the Constitution Court against the bill.
The Democrat Party says it also intends to launch legal action.
The assembly met at the National Institute of Development Administration (Nida) on Sunday.
The civic groups which make it up say the political reform body will work in parallel with the government's reform assembly to push for a "just, secure and happy society".
Its formation is seen by observers as a snub to Prime Minister Yingluck Shinawatra's political reform initiative that kicked off in the absence of the opposition Democrat Party.
One of Part's leaders, former core member of the People's Alliance for Democracy (PAD) Somkiat Pongpaiboon, said yesterday the assembly believes the borrowing bill contravenes the constitution.
Mr Somkiat said the assembly will hold forums in 77 provinces nationwide to gather public input.
The bill, which authorises the Finance Ministry to seek loans totalling 2 trillion baht for infrastructure development projects, passed its third reading in the House of Representatives on Friday night by a vote of 287-105.
The bill is expected to be passed on to the Senate for deliberation by senators this week.
Thaweesak Sutakawathin, president of Nida's teachers council, said government spending is regulated by budget laws, but the borrowing bill evades the regular budget procedure and the normal fiscal system.
He said the assembly does not oppose the development projects, but it was wrong for the government to manage spending by avoiding proper budget channels.
Pichai Rattanadilok Na Phuket, a lecturer at Nida's school of social and environment development and one of the Part's leaders, said the assembly has paid close attention to a wide range of issues covering politics, environment, and energy which affect the public.
The borrowing bill will have long-term repercussions for future generations, Mr Pichai said.
Mr Pichai said the reform assembly yesterday also discussed other issues including the rising cost of living, the amnesty bill, and the charter amendment bill.
The assembly is also monitoring the government-initiated reform assembly which has invited prominent figures to discuss ways to heal the political divide, Mr Pichai said.
Preeda Tiasuwan, head of the Businessmen for Democracy and Environment Club, said the executive and legislative branches are unable to address the country's problems properly.
The People Assembly Reforming Thailand wanted to do its part.
Mr Preeda, chairman of Pranda Jewellery, stressed the need to decentralise power so people can determine their own future.
Land should be distributed to the landless poor, who can make better use of it.
It should not be kept in the hands of only a few.
Meanwhile, a Senate committee on monetary, fiscal affairs and banking has released a study on populist policies and public debt.
The study showed the Yingluck Shinawatra government's populist policies have created a fiscal burden of more than 544 billion baht during the past year.
The policies include tax reductions for first-house buyers, which created a fiscal burden of 12 billion baht, a tax rebate for first-time car buyers, which led to a fiscal burden of 30 billion baht, a cut in corporate income tax, which created a burden of 52 billion baht.
The Democrats will today launch their "Thai Khem Khaeng 2020" national development master plan to challenge the borrowing bill.
Earlier, it announced its move to petition the Constitution Court to consider whether the bill violates budget control regulations in the charter.
Democrat spokesman Chavanont Intarakomalyasut said the Thai Khem Khaeng 2020 plan would serve as a model showing how money under budget laws could be better spent.
About 90% of the government's 2-trillion-baht scheme will go on rail development, but under the Thai Khem Khaeng 2020 plan, money will be spent more broadly, on education, public health and transport.