The Higher Education Free Speech Bill would introduce a requirement for universities and student unions to protect freedom of speech, including a new "free speech champion" who would investigate no-platforming cases.
The Bill, first introduced by former education secretary Gavin Williamson, is due to have its third reading in the Commons on Monday.
Houghton and Sunderland South MP Bridget Phillipson, who is Labour’s shadow education secretary, said the focus on free speech on campuses is a distraction from the Government's "failure" on wider issues.
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She said: "It's clear to me that all of this is Government ministers seeking to distract from their total failure on the wider challenges that we're seeing right across education - it's just pretty desperate stuff.
"Vigorous debate and open debate in our universities is really important.
"Of course it must cross a line where it comes to violence or intimidation or abuse.
"I think people understand that students want to protest, want to express their views, and that's right, that's not a new thing. I don't know why Government ministers are surprised that 18-year-olds finding their voice want to express their views quite strongly.
"The irony around the freedom of speech discussion is that it feels quite often that ministers are keen on freedom of speech unless you happen to disagree with them, at which point it's a problem.
"You either believe in freedom of speech or you don't."
She said it is "one of a long series of issues that the Government will surface when they've got nothing else to say".
She went on: "They've got nothing to say about our children's recovery, about the challenges that young people are facing around mental health, about how we improve our standards in all of our schools, for all of our students, so they then pick a fight with some students. I think it's pretty pathetic stuff."
Ms Phillipson added there is a "false divide" between university and vocational education, with ministers seeming to want to "pull up the ladder" when it came to a crackdown on low-quality degrees and minimum entry requirements for loans, as higher and further education minister Michelle Donelan has proposed.
Many young people do not face a "genuine choice" between university and vocational routes, Ms Phillipson said.
While around 50% of school leavers went on to higher education across the UK, she said that in her constituency of Houghton and Sunderland South "the number is much, much lower".
She added: "I find it frustrating that Government ministers seem to want to pull up the ladder and restrict opportunity.
"I don't think the Government should be closing the door to young people who've overcome adversity and now want to go and study at university.
"Government ministers seem intent on picking a fight all the time with universities. Our universities are a brilliant success story... they do tremendous work.
"The Government should recognise that our universities are a public good, not a political battleground.
"Young people end up caught in the middle of this, and they hear from the Government that university maybe isn't for them."
Ms Phillipson also said that given the impact of the pandemic and the "absence of a proper recovery plan from the Government", there could be "significant difficulties come summer" for pupils sitting exams.
"Many young people will be sitting exams this summer having received no additional support provided by the Government," she said.
"I think it's completely unacceptable and it's failing a generation of our young people."
She added that she welcomes the fact exams are going ahead.
Ms Phillipson went on to say that one of the key issues headteachers are raising with her is the impact of the cost-of-living crisis on resources.
"Whenever I speak with heads and school leaders, they tell me about the very difficult decisions they're being forced to take - cutting back on staffing, asking parents to provide stationery for their children, cancelling school trips. That's not what parents expect in 2022,” she said.