While there is general but not unanimous agreement that our current system is outdated, what we would change it to is quite contentious. If you want to get broad or near unanimous support for a given change, that will never happen.
Trudeau likely didn't realize how contentious this issue is. He likely believed that he could introduce a small change, test the waters, and then expand from there as people have given the issue more thought. The obvious contender for that is what Honourable Stéphane Dion had proposed years ago which is to keep everything else the same but switch from a ballot with a single "X" on it to a ranked ballot (Also known as Alternate Vote, or Instant Runoff).
Unfortunately the folks who spend all their time worried about how political parties are doing falsely claim this would exaggerate false majorities. These activists want a system where the seats in the house for a political party represent how people voted for political parties. They seem ignorant of fellow Canadians who vote for representatives from their riding, ignoring party affiliations, and don't believe that political parties can ever represent them. These voters don't believe claims that a party-focused PR system brings in "more women" or other groups not represented in parliament as they are in society, but believe it only brings in more passive party hacks. While not all PR systems are party focused, the marketing done by the PR representatives are party focused and thus those who don't trust political parties end up opposing PR as a concept.
There are many of us who (backed up by history) consider political parties to be ephemeral labels that are used as a temporary short-form for ideas. In a working democracy our representatives are not only free but expected to switch to another ephemeral label (cross the floor, or start a new party) if a party stands in the way of the MP representing their constituents. While some of these labels have been the same or similar over the years, what individuals and values the labels represent has radically changed over time.
These are my views based on decades of closely observing Canadian politics, and other people feel differently -- quite opposite at times. This political debate can get heated. Even though I sponsored the Fair Vote Canada website when they were first formed, I have recently distanced myself from that organization as I believe their focus on political parties and "PR or nothing" campaign is delaying electoral modernization in Canada.
Mr Trudeau also seemed unaware of the divisions in his own party on this. I know of Liberal members who favor FPTP as this is the system (not Alternate Vote) that has favored the Liberals who can run on their "don't split the vote" campaign. I know of Liberal members who oppose MMP or any other system that puts political parties on the ballot as they believe political parties have too much power already. There are Liberals active within "Fair" Vote Canada who agree with their "PR or nothing" campaign. We all know of Liberals including Dion and Trudeau who have publicly spoken in favor of ranked ballots (first step being keeping the system the same as it is now with Alternate Vote, and potentially introducing multi-member district STV or an MMP-style second ballot question on party once the public is ready for more radical change). I don't think there is broad support for any specific change (or lack of change) within the Liberal party itself, so this can't be expected of Canadians generally.
I don't know how this will turn out.
- The Conservatives like the current system as it has given them many false majorities. They push for a referendum knowing that this will mean the system can't change given how divided Canadians are on the issue.
- The NDP and Greens have falsely equated the election promise to being a system of proportional representation because Mr. Trudeau mistakenly used the "make every vote count" phase around people who believe that this phrase is equivalent to saying Proportional Representation. These groups can't even be trusted doing or reporting on polling given their confusion on language (deliberate or otherwise) will lead to inconclusive or invalid results.
- The Liberals are stuck in a messy place given there is nothing they can do (including doing nothing) that won't make many people angry. They can't go ahead with a simple change and not have someone claim they were lying about a misunderstood campaign promise, nor can they make more radical changes without having many people on a variety of sides of the debate saying they are destroying our democratic system. Whether they do or don't have a referendum there will be people suggesting they did the wrong thing.
- Many Canadians are throwing up their hands with a "pox on all their houses" type feeling given how divisive the issue has become.
While I'm not a fan of the Liberals, and campaigned against Liberals during the last election based on this issue, I kinda feel sorry for the predicament they put themselves in.