This is according to a document seen by Reuters shows.
The administration can continue using last year's budget for six months before the government theoretically goes into shutdown, the constitution says. That has not happened before.
The budget bill, which represented a delicate balancing act between the finance minister's drive to slash spending and lawmakers' demands for more money for projects, has been stalled since December.
Now, the non-partisan National Assembly Budget and Research Office (NABRO), a committee whose members include lawmakers from both lower and upper houses, is calling for a public hearing in which Okonjo-Iweala would be quizzed on her performance as finance minister before any budget vote.
Parliament's finance committee submitted 50 questions on the economy to Okonjo-Iweala last month, but lawmakers are not happy with her responses, the confidential NABRO document shows.
Africa's second-biggest economy and top oil producer has become more attractive to sovereign debt investors in recent years due to its fast growth, but they still worry about the tendency of its fractious and often corrupt politics to hinder economic reforms.
Political wrangling is expected to continue until elections next year and could damage public finances at a time when oil savings are dwindling and its currency, which has been largely stable, is under pressure during a selloff of emerging market assets.
Okonjo-Iweala, a former World Bank vice president, told Reuters the hold-up was down to "partisan politics".
"The budget should not be used as a weapon," she said.
Nigeria is already facing a political crisis over President Goodluck Jonathan's assumed intention to run in elections scheduled for February next year. That led five state governors and dozens of lawmakers to defect from the ruling People's Democratic Party (PDP) late last year and join the opposition All Progressive Party (APC).
The APC, which has one more seat in the House of Representatives than the PDP following the defections, has ordered its members to block the budget over an unrelated issue regarding insecurity in the Niger Delta.
The PDP still holds a comfortable majority in the Senate.
Yet many ruling party legislators are also preparing for a showdown over the budget, sources say.
"The budget's not likely to be done any time fast," said a source in parliament. "It's become really personal."
Okonjo-Iweala, in her second stint as finance minister, had already made some concessions in the 28.6 billion US dollar budget by raising the benchmark oil price - above which Nigeria saves money it earns from oil exports - to free up more money for spending.
The NABRO document shows lawmakers in no mood to accept Okonjo-Iweala's responses to their questions on the economy, accusing her of "an unfriendly and discourteous style of writing", disputing her data, and urging "a public hearing on the matters raised".
Any such hearing could delay the budget by weeks.
The questions the lawmakers say they want answered include why economic growth of above 6 percent has failed to lift more Nigerians out of poverty, and why the administration has cut capital spending when Nigeria is in need of infrastructure.
"There was always a risk politics would get so contentious as to delay the budget," said Standard Chartered's Razia Khan.
"I wouldn't be surprised if this doesn't go right down to the wire."