But he did argue that Obama has the chance to turn the situation around by stressing how the massive bill will be "paid for" - even though another stumbling block he cited was more conservative "Blue Dog" Democrats upset by the massive tax increase embedded in the House bill.
"Whether they're going to be able to get there [to a health care bill by the end of the year] is still unclear, Diane, but I think those who are counting it out right now, who are saying there is no way this is going to happen because July is tough, I think they are wrong as well," Stephanopoulos gamely argued.
"That's right," Sawyer agreed, "because there's still polling that shows that everybody thinks something has to be done, so that's still a motivator."
Stephanopoulos kept channeling the White House message: "That, that is the motivator, and I think the message the President is going to be bringing to Democrats today in these private meetings, to the country tomorrow in that press conference is, the costs of doing nothing are far too high, we're not giving up."
But it's not as if Obama has not already been strenuously making his case over the past several days, and the polls Stephanopoulos cited show support dropping in spite of the ongoing White House PR effort.
Here's the full exchange on the July 21 Good Morning America, which followed a report by White House correspondent Jake Tapper about Obama's appearance on PBS's NewsHour  and efforts to gain support among balking House Democrats:
DIANE SAWYER: Joining us now with "The Bottom Line," ABC's Chief Washington correspondent, host of This Week, George Stephanopoulos. Good morning, George.-Rich Noyes is Research Director at the Media Research Center.
GEORGE STEPHANOPOULOS: Hey, Diane.
SAWYER: August 8 recess. The President always wanted a bill by August 8. And will he get it?
STEPHANOPOULOS: I don't think so. The votes are not there right now. But the White House is going to pull out all the stops in these next couple of days, over this next week, to get it done. The President didn't want to say "crack heads" in that interview [with PBS's Jim Lehrer] - they're going to have to crack heads this week.
SAWYER: Bringing in Democrats - Democrats! How many are wobbling?
STEPHANOPOULOS: That meeting is almost certain to happen today. There are different groups of Democrats wobbling in different parts of the Congress. Today he's going to meet with House Democrats, the so-called "Blue Dog Democrats." They're the more conservative House Democrats, and they are very, very concerned that the bill that is moving its way through the House of Representatives has way too much in tax increases and not enough spending cuts. So the job there right now is for the President and the Democrats to come together in the House, bring down those tax increases, bring up the spending cuts, so you can get a bill that will pass the House. Even Speaker of the House Nancy Pelosi yesterday came out and said she thinks there are too many tax increases in that House bill.
SAWYER: Right, and not just the Republicans on the tax question. Polling is showing that the American people just don't believe that this is going to be a budget-neutral event.
STEPHANOPOULOS: And that is the big problem for the President and the White House right now. We saw our own poll yesterday, which indicated it was going in that direction. Today, USA Today and Gallup have similar numbers  showing [on screen] one, 50% disapprove of President Obama's approach on health care and - this is a big number here, Diane - 59% think there is just too much government spending. They think this is going to break the bank, that this is going to increase deficits. The President has said this bill has to be paid for.
SAWYER: And, is that what he's going to address in the speech [Wednesday night's press conference], that's why he's giving the speech?
STEPHANOPOULOS: That's one of the reasons he's giving the speech. One, he believes, and I think the White House believes, that the price of not acting is going to be severe, there is no question about that. But they also know right now that Americans are concerned, most of all, about the deficit and spending - they've got to hammer home that point, this will be paid for.
SAWYER: Does this also mean, if he does get a bill by the end of the year - and he said to me in our interview, "Absolutely I'm going to get that bill by the end of the year" - if he gets a bill, it's going to be a bare-bones bill, just a couple of provisions, tell everybody what they can expect as a baseline.
STEPHANOPOULOS: It's hard to know. There's few bottom lines out there that have to happen. The President's laid out his bottom lines: number one, the bill has to move towards covering everybody; number two, it has to move towards controlling costs for everyone; and then, three, it just has to be paid for. Now, whether they're going to be able to get there is still unclear, Diane, but I think those who are counting it out right now, who are saying there is no way this is going to happen because July is tough, I think they are wrong as well.
SAWYER: That's right, because there's still polling that shows that everybody thinks something has to be done, so that's still a motivator.
STEPHANOPOULOS: That, that is the motivator, and I think the message the President is going to be bringing to Democrats today in these private meetings, to the country tomorrow in that press conference is, the costs of doing nothing are far too high, we're not giving up.