The Christian Science Monitor thinks that the Democrats wrote their infrastructure plan as a "political bridge to President Trump." Fox News thinks that Trump might "get on board" the Democrats' plan. Statements like these show that many reporters--and by extension members of the public--haven't yet figured out the real issues behind the infrastructure debate.
As Business Insider points out, there's a bigger difference between the two sides over "how it's paid for" than "what gets built." The Democrats want the federal government to spend a trillion dollars, money it would have to borrow. Trump wants private investors to spend their own money. Never the twain shall meet.
But Business Insider doesn't understand how Trump's idea will work. If Trump is going to rely on the private sector, it says, then only projects that generate revenue will be built because "projects that don't generate revenue for the private sector generally don't get financed." But there are two kinds of public-private partnerships. The kind that Business Insider is writing about is called demand risk because the private partner takes the risk that tolls, fares, or other user fees won't repay the cost.
The second kind is called availability payments because the government agrees to pay the private partner the cost of the project over time, whether or not anyone pays user fees or even uses it at all. In this kind, the public takes the risk. While I much prefer the demand-risk form because I think nearly all infrastructure ought to be paid for out of user fees, Trump may be happy to go with availability payments so long as state or local governments are making the payments, not the feds. Democrats in Congress don't like either one because they short-circuit their ability to appear to give gifts to their constituents.
The third issue that many people don't understand is the difference between Trump and the Democrats over jobs. The Democrats' plan estimates that number of jobs that will be created by spending money on construction and maintenance. They used a simple formula: each billion dollars of spending generates 13,000 jobs (about $76,000 per job). Of course, they really mean job-years, and that formula works as well for digging holes and filling them up as for building roads or water lines.
Trump is less concerned about the immediate jobs than whether projects generate long-term benefits for the economy. Digging a hole and filling it up creates short-term jobs, but if there are no jobs after the project is done, it wasn't worth it. A transportation improvement that generates new travel will generate jobs in the long term. A transportation project that merely substitutes one form of travel for another will generate few, if any, long-term jobs.
So there are three irreconcilable differences between Trump and the Democrats: where the money comes from in the short run (public vs. private); how it is financed in the long run (feds vs. state & local); and what kind of jobs they should shoot for (short-term vs. long-term). In short, while both sides talk about "trillion-dollar plans," they mean very different things.