That would throw the country into financial chaos and, ultimately, cause it to leave the eurozone, with unpredictable consequences for the region.
Several bills were being submitted to Parliament on Thursday night, including restructuring the banking sector, setting up an "Investment Solidarity Fund," and restricting banking transactions in times of crisis.
Together, they will make up at least part of the alternative plan Cyprus hopes will secure bailout money. The lawmakers said the bills would be discussed and potentially voted on Friday morning.
The pressure has increased since Parliament on Tuesday rejected an earlier proposal to seize up to 10 percent of people's bank accounts. Banks have been shut since last weekend to avoid a run and will not open until Tuesday at the earliest.
Uncertainty was growing among Cypriots as the deadline approached and it became clear that the second-largest bank, Laiki Bank (or Cyprus Popular Bank), would be restructured.
Queues of 40 to 50 people formed at Laiki ATMs, on which daily withdrawals were capped at 260 euros ($340) per person from 700 euros ($906). Although ATMs have been functioning, many often run out of cash.
"We need cash. We have families, children, grandchildren, and expenses, and the banks have been closed since Saturday," Andri Olympiou said after withdrawing money from a Laiki branch in Nicosia, the capital.
The central bank governor, Panicos Demetriades, urged lawmakers to vote immediately on a legal framework bill to rehabilitate Cyprus's banking sector.
The bills include restructuring Laiki, a move that would raise an estimated two billion euros out of the total 5.8 billion euros Cyprus needs, according to local media.
Once it is done, the country would be in a position to guarantee all deposits up to 100,000 euros ($130,000) - the EU-wide limit for bank guarantees.
Officials said the restructuring would split Laiki into two, with a "bad bank" taking over its soured investments and a "good bank" retaining the healthy ones.
Setting up a bad bank is a strategy that has been used before in Europe's financial crisis, by Ireland and Spain. A bad bank is tasked with recovering as much money as possible from the investments.
Without the restructure, Laiki would collapse and drag down the rest of the banking system and the economy, Demetriades said.