A new NPR/PBS NewsHour/Marist poll shows the Senate health-care bill is deeply unpopular — and not just among Democrats. (Peter Stevenson/The Washington Post)

This post has been updated.

Amid a revolt against the Senate health-care bill, supporters have seized upon something of a last-ditch argument: Whatever you think of this bill, they say, you owe it to your voters. Republicans have been promising for years to repeal and replace Obamacare, the argument goes, and not passing this bill will mean they will have broken their promise.

There is one big problem with that strategy: The GOP base doesn't seem to see it that way.

Not only aren't Republican voters particularly keen on this bill, but polls suggest they wouldn't even blame their Republican members of Congress for failing to close the deal.

To wit:

  • A new Marist College poll conducted for NPR shows people overall disapprove of the Senate bill 55 percent to 17 percent. And even Republicans and those who approve of Trump are pretty split. The GOP approves only 35-21, and Trump backers approve only 36-28.
  • Asked who would be to blame if it doesn't get done, 50 percent of Republicans would blame Democrats in Congress, while only 20 percent would blame Republicans in Congress, and only 6 percent would blame President Trump. Even tea party supporters — perhaps those most adamantly opposed to Obamacare — would blame Democrats over Republicans, 39-30.

  • A new Quinnipiac University poll shows just 6 percent strongly approved of the bill, while 46 percent strongly disapprove. Even among Republicans, just 18 percent strongly approved of it, while 11 percent disapproved strongly.
  • A new poll conducted for the pro-Obamacare group Save My Care by the Analyst Institute asked whether people would prefer senators who “vote for this bill to keep their promise of repeal” or “vote against this bill because it will cut coverage for millions and increases premiums and deductibles.” Just 48 percent of Republicans say they still want a senator to vote for it; the other 52 percent prefer that they vote against it (27 percent) or don't know (25 percent).

The idea that anybody is pining for this bill and will punish their GOP members of Congress for not passing it just isn't borne out in these numbers. There will perhaps be Republicans disillusioned with their party's failure to deliver on a campaign promise, but these polls suggest they will be relatively few and that the lion's share of them will blame Democrats anyway.

The pro-Trump outside group America First Policies has attempted to apply pressure on one of the bill's chief GOP critics, Sen. Dean Heller (R-Nev.), by running an ad campaign pushing him to vote for it. But polls like this suggest members in competitive states like Heller (who faces reelection next year) pretty clearly have much more to worry about from general election voters than primary ones. And perhaps tellingly, Heller doesn't seem particularly perturbed by the pressure; he doubled down on his opposition to the Senate bill on Tuesday night, big time.

I've written before that this is the bill that nobody really wants all that badly. These numbers suggest that's even true of the GOP base. And when it comes to convincing skeptical members that this is something they need to pass, warts and all, that makes for a far less compelling case.