The Government will try to delay a plan to refer Boris Johnson for a probe into whether he misled Parliament over the Partygate scandal.
The Prime Minister's diplomatic trip to India on Thursday is set to be overshadowed by the row back home.
Tory MPs will be on a three-line whip on Thursday to kick any decision to investigate Mr Johnson into the long grass.
Labour accused the PM of trying to "rig the rules" to deflect from his own law-breaking.
The Tories have published an amendment to the Opposition bid so that MPs will only get a say after Sue Gray has published her report.
With an 80-strong majority, the Government's brazen attempt to kill the plan for now is likely to be successful.
However, the move is not risk-free for Mr Johnson as it potentially gives MPs another chance to vote for a probe in the weeks ahead.
Disgruntled Tories may be more willing at that stage - after further Partygate fines and poor local election results - to give one the green light.
A spokesperson said: "This Government has tabled an amendment to Labour's motion which says that consideration of this matter should take place after the conclusion of the police investigation, and the publication of the Cabinet Office report, allowing MPs to have all the facts at their disposal."
More than a dozen Tory MPs had been expected to abstain on Thursday further denting the PM's authority.
They included Tory MP Sir Charles Walker, vice-chairman of the influential backbench 1922 Committee, who said: "If the fines keep racking up there is only so long that the Prime Minister will be able to lean on his party for support."
But many Tory MPs are understood to be uneasy that blocking an investigation into the Partygate row would prompt comparisons with the Owen Paterson saga.
Labour had warned that a failure to support their motion will mean targeted campaign attack ads in their local areas.
A Labour source said: "Tory whips obviously knew that they couldn't vote this down.
"They clearly haven't learnt a thing from the mess they got into over Owen Paterson.
"Boris Johnson is trying to rig the rules to deflect from his own law-breaking.
"Any Tory MP who votes for this is voting for a cover-up".
The standards committee, which would conduct any probe, has the power to summon reports and documents, meaning MPs could request to see the full Sue Gray report into lockdown gatherings at the heart of Government.
It also means they can ask to see the 300 photographs the top civil servant handed over to Scotland Yard as evidence.
Mr Johnson could be found in contempt of Parliament - like War Secretary John Profumo after he lied about an affair in 1963 - and if found guilty could even be suspended from the Commons.
Labour had attempted to remove some of the obstacles preventing Tory MPs from backing the move, which has the support of the main Opposition parties.
They said that any probe should not begin until the Met investigation has concluded.
Labour MP Chris Bryant, chair of the committee, had recused himself from any inquiry after Tory whips told waverers he had already "prejudged" the outcome by speaking out on Partygate.
Mr Starmer said: "We are urging Conservative MPs to do the right thing: to respect the sacrifice that their constituents made during the pandemic, to say that the public were right to follow the rules, and to vote in the national interest, not under pressure from the party whips."
Lib Dem leader Sir Ed Davey added: "Conservative MPs should think carefully before voting to block an investigation into Boris Johnson's lies.
"The public won't stomach another Conservative stitch-up that drags our democracy through the mud just to protect one of their own."
Chancellor Rishi Sunak also left the country on a visit to the US, meaning he too will miss today's crunch vote.
