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(CNN) —  

It’s getting very hot in the hot tub for Senate Republicans at the moment.

On Tuesday, the Democratic-majority House will vote to disapprove of President Donald Trump’s decision to declare a national emergency along our Southern border. Once that happens, the Senate, by law, will have 18 days to take a vote of its own on the privileged resolution.

And at the moment, the momentum is moving against Trump and Senate Republican leaders – raising the possibility that the President could be forced to issue the first veto of his tenure on what is widely seen as his biggest campaign promise, an embarrassing moment to say the least. The latest crack in Republican support for Trump’s wall – or, at least, his decision to use his national emergency powers to funnel previously allocated funds to build the border barrier – came Monday, when North Carolina Sen. Thom Tillis (R) announced that he would vote for the disapproval resolution. Here’s a bit of what he wrote in a Washington Post op-ed announcing the decision:

“As a U.S. senator, I cannot justify providing the executive with more ways to bypass Congress. As a conservative, I cannot endorse a precedent that I know future left-wing presidents will exploit to advance radical policies that will erode economic and individual freedoms. These are the reasons I would vote in favor of the resolution disapproving of the president’s national-emergency declaration, if and when it comes before the Senate.”

That makes Tillis the second Republican senator who will side with Democrats on the disapproval resolution when it comes to a vote. (Maine Sen. Susan Collins said last week she would support the disapproval measure.) A third – Alaska Sen. Lisa Murkowski – has now come out definitively in favor of the resolution, telling reporters Tuesday that she will support it.

Trump sought to keep wavering Republicans in line with a tweet Monday: “I hope our great Republican Senators don’t get led down the path of weak and ineffective Border Security. Without strong Borders, we don’t have a Country - and the voters are on board with us. Be strong and smart, don’t fall into the Democrats “trap” of Open Borders and Crime!”

Assuming that all 47 Democrats – including the two independents who caucus with Democrats – vote for the resolution that means that only one more Republican needs to defect in order to put the disapproval resolution on the President’s desk. (No Democrat has come out and said they will oppose the measure; the two most likely to do so – if any do – are West Virginia Sen. Joe Manchin and Alabama Sen. Doug Jones.)

Sen. John Cornyn (Texas) told CNN’s Ted Barrett on Monday that while he would oppose the measure, he expected it to pass the Senate – forcing Trump into a veto that would hold due to the fact that neither chamber would have the two-thirds majority to overturn it.

Some of that is expectation-setting by Cornyn, trying to lower expectations to the point where if the measure of disapproval does pass the Senate he – and Senate Majority Leader Mitch McConnell (Kentucky) – can try to downplay the impact or their surprise.

But let’s play this out. There are, at present, at least 50 votes for the national emergency disapproval resolution. Where might the other one come from? (The measure would need 51 votes to pass.)

The fact that Collins and Tillis are already on record as vote in favor of the disapproval resolution is telling when trying to sniff out who else might defect. Both are up for reelection in 2020 in states that are swing-y. A vote against the disapproval proposal would surely be fodder for their eventual Democratic opponents, who would use the vote to cast the incumbents as unquestioning backers of not just a proposal that a majority of the country opposes (Trump’s border wall) but a President who is not terribly well-liked in either state.

By those standards, here are the Republican senators who might have the strongest political reason to be for the disapproval measure:

1) Cory Gardner (Colorado): Gardner represents a state Trump lost in 2016 and is a major target for Democrats in 2020. He hasn’t declared a position yet on the resolution but did say last week that “Congress is most appropriately situated to fund border security.”

2) Martha McSally (Arizona): McSally lost the 2018 Senate race to Sen. Kyrsten Sinema (D) but was appointed to fill the vacancy caused by Sen. Jon Kyl’s (R) resignation in mid-December. That makes McSally potentially vulnerable as she seeks the remainder of Kyl’s term in 2020. Her decision is particularly fraught because Arizona, a border state, has long been on the forefront of the national immigration fight, with lots of the most outspoken supporters of Trump’s border wall making lots of noise in the state. (Former Maricopa County Sheriff Joe Arpaio, I am talking about you.) Given that, a vote in favor of the disapproval resolution could be the spark of a serious primary challenge to McSally. But voting against the measure could be problematic in a general election too. McSally has stayed very quiet on this issue but is going to have to make up her mind soon-ish.

3) Joni Ernst (Iowa): The Hawkeye State went for Trump in 2016 but moved strongly back to Democrats in the 2018 midterms. Democrats lost their top recruit in the form of former Gov. Tom Vilsack (D) last week, but are pursuing Rep. Cindy Axne among others. While recent polling suggests the freshman Ernst is in solid position in 2020, she still needs to be mindful of the shifting dynamics in her state. It’s not surprising then that Ernst has yet to say much publicly about how she might vote on the resolution.

Taken together, the conclusion is simple: The math and the momentum are working against Senate Republicans right now. Of course, 18 days is a decent chunk of time for McConnell and Cornyn to turn this around and avoid having Trump’s first veto as President be on his border wall.

But as of today, that appears to be exactly where we are headed.

CORRECTION: This story has been updated to correctly state the votes needed for the disapproval measure to pass. It is 51.