You are close on this analysis.
But, I would suggest the Dems. came forward with a plan first, put the gauntlet down that if he backs THEIR plan, he will get their support.
Reality, he shouldn’t back THEIR plan for all the reasons you stated.
BUT, it then gives them a way to scream, shout, and pontificate how the President lied about infrastructure plans. Watch...this little democrat dog and pony show is a political trap.
So what is the wisdom here? Back it or negotiate them out of their own plan? How much/far do you trust Trump? Trump is for America, united, together. Do we trust him enough to let him slice and dice the democrat plan?
Reminds me of the Dem hag (sorry, I cannot remember which Dem hag it was) that basically came out and said ‘we will work with Trump if he does what WE want’. Just a couple of weeks ago....wish I could remember who said it.
Do your own plan and use bits and pieces of their plan to peel enough of them away if needed to pass the overall plan.