OTTAWA -- Civil service unions say they will hold the government's feet to the fire now that the Liberals have promised to replace the troubled Phoenix pay system with a compensation system that works.

Federal employees are rallying in cities across the country today, marking the second anniversary of the disastrous launch of Phoenix.

The lunch-hour protests come a day after the Trudeau government announced it will build a new pay system and eventually scrap the IBM-built Phoenix program.

While many workers say they're encouraged that the pay system will be replaced, their unions say they won't let their guard down until the government delivers on its pledge.

The Phoenix pay system has been a nightmare for tens of thousands of civil servants since it was formally launched two years ago.

Fixing Phoenix, which has left many government employees underpaid, overpaid or not paid at all, is, so far, expected to cost upwards of $1 billion, with estimates that the final tally could go much higher.

Tuesday's federal budget also provided indications that it could take more than two years to develop, test and ultimately launch a new pay system.

The Public Service Alliance of Canada, which organized the rallies, said it's still concerned that the Trudeau government didn't provide an exemption to ensure that employees who were overpaid don't have to return the gross total of those overpayments.

PSAC said its members complied with government instructions to report overpayments by mid-January or risk having to pay back more money than was deposited into their bank accounts. But thousands of civil servants could still be forced to pay back the gross overpayment amounts because of the government's inability to process their reports, the union said.

The government has agreed to consider changing tax laws for the 2018 tax year to allow public servants who were overpaid to repay the net amount, rather than the gross amount.

The Professional Institute of the Public Service of Canada (PIPSC) said it will press the government to mobilize its own IT professionals to build a new working pay system.

"I see this as a glimmer of hope in a long two years of constant stress and financial worry for our members," PIPSC President Debi Daviau said of the government's pledge to replace Phoenix.

"We told them our members had lost confidence in Phoenix. We said nix Phoenix -- we deserve better and they have listened."

PIPSC has said it could build a replacement for Phoenix within a year.

The budget allocates an additional $431 million over six years to address problems created by Phoenix, on top of the $460 million already committed to both implement the pay system and resolve subsequent problems.

The budget set aside $16 million to begin the process of replacing the troubled system.

And the Canada Revenue Agency will get $5.5 million to conduct income tax reassessments for individuals affected by Phoenix.

But the costs are likely to escalate under a government pledge to also work with the unions on compensating employees for mental and emotional stress caused by the Phoenix foulups.

When it was approved in 2015 by the previous Conservative government, officials said the pay system would save taxpayers about $70 million annually by streamlining and consolidating pay systems across dozens of departments and agencies.