A victory for Labour in Wednesday's vote could topple May's government, but her administration is likely to survive thanks to a deal May reached this week with 10 lawmakers from Northern Ireland's Democratic Unionist Party.
Corbyn has demanded that nurses, teachers and emergency services workers should receive better pay and more funding for the services they provide.
She said that the case for a cross-party commission had become even stronger after the Conservatives lost their majority at the election.
Labour leader Jeremy Corbyn, whose party has 262 lawmakers, said his party would submit an amendment to May's legislative plan in an attempt to end cuts to the police and fire service and to give emergency and public sector workers a pay rise.
The Royal College of Nursing (RCN) general secretary Janet Davies said: "Hours after nursing staff have staged protests in 30 towns across the UK, MPs will have the first opportunity to show they are listening".
"It stands in the way of filling the 40,000 vacant nurse posts in England and must be scrapped this summer".
Speaking to Sky News, Mr Corbyn said: "Cuts in local government expenditure have a price to pay".
Around five million workers employed in local authorities, schools, hospitals and job centres have seen their wages fall in real terms following two years of a pay freeze and four years with salaries capped at a below-inflation 1 per cent. It's also made it more hard to recruit and retain staff in key public services.
Mostly sunny, chance of scattered showers and thunderstorms — TODAY'S FORECAST
THROUGH INDEPENDENCE DAY: Routine summer weather is expected to continue this weekend and through the Independence Day holiday. The extended forecast for Tuesday and Tuesday night is for cloudy skies with a few showers and isolated thunderstorms.
"What the tragedy of Grenfell Tower has exposed is the disastrous effects of austerity, this disregard for working-class communities, the awful consequences of deregulation and cutting corners", he said.
Det. Supt. Fiona McCormack, who is leading the investigation, said, "We are many months from being able to provide a number which we believe accurately represents the total loss of life inside Grenfell Tower". The public sector pay gap is hitting recruitment and retention across the public sector.
"In other parts of the United Kingdom, fire services would, quite frankly, struggle to commit the same level of life-saving resources and personnel that London was able to".
"Those cuts to the fire service have meant that there are 11,000 fewer firefighters. The cladding of tower blocks began under the [Tony] Blair government".
"We will seek to use every mechanism in parliament to defeat them on those policies", the spokesman said.
May's Conservative Party said in a statement that it had protected police budgets, while the number of fires had fallen by half in the past 10 years.
"We have also given the police and intelligence agencies given the powers they need to respond to increased threats and keep people safe".
In the wake of the Labour leader Jeremy Corbyn's general election popularity surge, many parents are now considering the name Corbyn for their next baby, a survey has revealed.