The Home Secretary also accused Labour of attempting to "delay, disrupt or sabotage" the bid to end the small boats crisis.
Mr Cleverly insisted ministers "remain focused on not letting that happen" and getting flights off the ground to discourage migrants from risking their lives in dinghies.
Prime Minister Rishi Sunak's flagship Rwanda Bill returns to the upper house today for another Parliamentary showdown, with peers set to "hold out for as long as possible" in an effort to water down the Government's plans.
The Home Secretary said last night: "It has always been illogical to argue the Rwanda scheme won't work while trying everything and anything politically to ensure it can't.
"The more this Bill progresses, the more worried Labour get that it will work and the more we've anticipated deliberate efforts from Labour to delay, disrupt or sabotage the scheme. We remain focused on not letting that happen and hope their Lordships recognise it's time to let this Bill pass, so we can continue to stop the boats, and save lives." MPs on Monday night overturned 10 amendments that had been passed by the House of Lords.
Home Office minister Michael Tomlinson accused peers of tabling "wrecking amendments", while Tory grandee Sir John Hayes questioned whether the Lords were "clueless or careless" about what is happening with immigration.
Conservative MP Alexander Stafford warned weakening the Bill would be an "open-door policy to let human traffickers traffic people illegally into our country".
But Lords have vowed to continue fighting the deportation plan for "so long that the Government can't get any of its flights to Rwanda".
Lord Charlie Falconer, Justice Secretary in Tony Blair's Government, said: "A win for us is holding out for as long as possible.
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