(CNN) The Senate returns for a critical three-week period when Republicans will try to salvage their health care bill. But it's clearly in deep trouble and they might not be able to save it.

Things are looking especially tough after the bill hung out there over the recess (which Senate Majority Leader Mitch McConnell badly wanted to avoid) and it got battered by voters and senators.

Watch Tuesday's Senate lunch -- that's when we might get the first real indications of the week on which direction leadership is moving, and it'll be an opportunity for leaders to take the temperature of the conference on how they're feeling after the week-long recess.

Maybe the clearest sign that things aren't looking good? President Donald Trump's tweet Monday morning : "I cannot imagine that Congress would dare to leave Washington without a beautiful new HealthCare bill fully approved and ready to go!"

CNN's latest whip count on the "no" votes: 10

At least 10. Sen. John Hoeven of North Dakota became at least the 10th GOP senator to publicly oppose the bill in its current form with remarks he made to local media and a public statement released during the July 4 holiday.

*First caveat: 10 = only the Republicans who have publicly said no. There could be more, and other Republicans -- while perhaps not saying directly that they'd oppose the legislation as written -- described concerns or reservations they had about the current proposal.

*Second caveat: Plenty of the "no" folks have said they want to get to a yes, and some ultimately could.

What's the deal with McConnell?

What he said in Kentucky last week: Republicans might need to work with Democrats to prop up Obamacare if they fail to pass repeal and replace legislation.

No, McConnell isn't giving up on health care, and he's not yet close to pulling the plug. (And these weren't new comments -- McConnell has brought up the possibility of having to work with Democrats to stabilize markets the day he delayed the vote two weeks ago.)

Two ways to read McConnell's comments:

This has been a genuinely difficult process. The needle that he's trying to thread to get to 50 "yes" votes is very, very tough. It's not a secret that there is real frustration about how long the health care exercise has dragged on.

This is a warning shot to Republicans -- They can either suck it up, and vote for a bill that isn't perfect (and it's never going to be perfect for everyone). Or they can let the bill fail and stomach the political reality of reneging on a promise they've been making for years and years -- and the fact that the next necessary step would be to work with Democrats to do damage control on Obamacare.

What happened over the July 4 recess?

JUST WATCHED Collins still a 'no' on GOP health care bill Replay More Videos ... MUST WATCH Collins still a 'no' on GOP health care bill 00:53

Exactly as McConnell had feared and expected -- Senate Republicans got an earful over the July 4 recess. Just a sampling of the political heat GOP senators got when they went home last week:

Hoeven made clear he was against the bill.

Sen. Susan Collins: People in Maine are telling her "they don't want me to support it."

Sen. Jerry Moran: Said at a town hall in Palco, Kansas, that he's still a no , and that the bill would hurt rural communities.

Sen. Dean Heller, who is currently a "no" on the bill, got yelled at by a man back home to vote for the bill. So the pressure goes both ways.

Protesters cropped up everywhere: Outside Sen. Pat Toomey's office; at a Sen. Ted Cruz event in Texas and inside two offices of Sen. Rob Portman in Ohio

What happened over the weekend?

Sen. John McCain did not sound optimistic about his party's chances when he told CBS' John Dickerson on "Face the Nation" when he said the health care proposal was "probably going to be dead."

"I fear that it's going to fail, and then we should convene a Republican Conference and say, what are we going to do? Introduce a bill," the Arizona Republican said Sunday. "Say to the Democrats, here's a bill. It doesn't mean they don't -- that they control it. It means they can have amendments considered. And even when they lose, then they're part of the process. That's what democracy is supposed to be all about."

Also Vice President Mike Pence -- who's been active with Hill Republicans' health care discussions -- went horseback riding Saturday with Vice Chairman of the Senate Republican Conference Roy Blunt of Missouri as well as another crucial White House voice on health care: Seema Verma , administrator of the Centers for Medicare and Medicaid Services.

Thanks @RoyBlunt for joining @SeemaCMS @SecretaryZinke & me on ride thru Rock Creek Park & thanks to @usparkpolicepio for your work everyday pic.twitter.com/rWSM0Gyznh — Vice President Pence (@VP) July 8, 2017

What changes could be made to the bill?

Short answer is we don't know yet what the revised bill will look like. Those conversations will have to happen this week. But we do know at least two potential revisions to the bill that were sent to the Congressional Budget Office for scoring before members left town for the July 4 recess:

The Cruz amendment: Known as the "consumer freedom" amendment, it would allow insurers who offer plans under Obamacare to also offer plans that are unregulated under the law. (Conservatives like this, because they say it would lower premiums; critics -- including some moderate Republicans -- hate it, because they think it means skyrocketing premiums for the sick, as well as weakened protections for those with pre-existing conditions.)

Flexibility for Health Savings Accounts: Another provision that conservatives find appealing, it would offer more flexibility on how people can use HSAs, including using them to pay for premiums.

Don't expect that Cruz amendment to be a silver bullet. A telling comment from one GOP aide last week : "I think there's very little interest in the caucus in touching pre-existing conditions, so I have a hard time seeing the addition of the 'Consumer Choice Amendment.' And outside health policy folks have said that would set up a death spiral for the markets."

Asked about the Cruz amendment, Marc Short, White House legislative affairs director, said: "The White House is very comfortable with the policy. I think the question we all need to address is does it add votes or subtract votes?"

'We'll have a better sense this week after it is scored" and after Cruz talks with more senators himself.

What is the White House saying?

Short acknowledged that the messaging around the health care repeal effort has not been strong and faults all parties involved -- including the administration and congressional Republicans.

"I think it's fair to say the messaging throughout has been underwhelming, collectively, among Republicans," Short told CNN over the weekend. "It's a complicated subject."

Short said a lot of things were under discussion when it comes to how Trump might engage in this sales effort, but was reluctant to say for sure what the President would do beyond additional phone calls.

"You might see the President travel," he said. "You might see more messaging coming from him too." Short would not expand on what that messaging could look or sound like.

If the President does travel to try to sell the bill, he is likely to visit states of wavering Republicans, like Ohio or West Virginia -- though there are no plans for travel set in stone.

A vote next week?

There will be a vote when McConnell decides he has 50 "yes" votes. He's not there yet.

Talk from the White House of a possible vote next week? Just remember how many times the White House predicted votes when the House was considering its bill earlier this year, and how many times those predictions were not accurate. The White House doesn't determine the Senate schedule.

When will we see new CBO score(s)?

Still unclear. But, Senate GOP leaders have been in constant touch with CBO -- all so that when they're ready to pull the trigger, they can get a score from the CBO as quickly as possible.

Short said he expects the CBO score on the latest drafts in the next seven to 10 days.

"This week will be more focused on continuing to talk about the policy that is in the bill with the various senators that are undecided," he said.