I don't think they think they can use Republican votes for anything. That would be stupid. As you rightly say, nobody will remember who voted for what. You're dead correct that we have waaaay too many examples of Republican officeholders taking credit for shit they flamboyantly opposed (e.g., the Biden Infrastructure Act).
They think that without the ACA subsidies, the cost of healthcare will go up both this year and, importantly, next year. The premiums for 2027 are going to come out right before the midterms, and they're going to be catastrophically awful. Trump and the Republicans will be rightly blamed--not because of anything anybody voted for/against, but for the far more basic reason that a Republican is in the White House.
That's why I say it is a cynical play. And I love a cynical play. Because those are really the only plays that work.
This is what happens when elected officials try to play pundit. They just can't help themselves. They love to tell you how much more they understand about electoral politics than you do. But playing pundit gets in the way of effective messaging.
So you're right. They need to cut that shit out. The message is the Republicans were going to starve people, and we couldn't let that happen. Period. Then shut the fuck up.
How's that going to play in the next election, a CNN reporter might ask? "I don't really know, and it really doesn't matter--the Republicans were going to starve people, and we couldn't let that happen."
Are you concerned that your base is going to be angry that you didn't get more, an MSNBC correspondent might enquire? "I's hope not, but it really doesn't matter--the Republicans were going to starve people, and we couldn't let that happen."
But these people are all fucking assholes who are super-eager to let you know that they know more than you do. Dumb fuckers.