Here's Mitch McConnell's biggest problem in the impeachment trial

And at the moment, under the initial rules for debate proposed by McConnell on Monday night, the trial could actually wrap up by the middle of next week.

There's just one problem with McConnell's speedy timetable: A large majority of Americans -- including a plurality of Republicans -- believe new witnesses who did not testify during the House proceedings should be allowed to appear in the Senate trial.

In new CNN polling, nearly 7 in 10 Americans (69%) support new witnesses being allowed to testify. That number includes 86% of self-identified Democrats and 69% of political independents. Most intriguingly/importantly, it also includes 48% of Republicans who say they want to hear from new witnesses -- higher than the percentage 44% who say they do not want any new witnesses to be called.

Now, if past is prologue, McConnell won't care all that much about these poll numbers. He's someone uniquely focused on his own 53 senators and whether or not he can depend on them to provide majority support for the various rules that he will try to pass over the coming days and week(s).

But McConnell's math could well be affected by numbers like these. Because know who will be paying very close attention to how the public feels about witnesses?

* Sen. Cory Gardner (Colorado), who is up for a second term in November in a state Hillary Clinton won in 2016

* Sen. Martha McSally (Arizona), who trails her likely Democratic opponent this fall in almost all available polling

* Sen. Susan Collins (Maine), who will face the toughest race of her career this fall

* Sens. Joni Ernst (Iowa) and Thom Tillis (North Carolina) who sit in swing states and are up for new six-year terms in November.

All five of those senators don't have the luxury of ignoring public sentiment in this incredibly high-profile Senate trial. Their chances of keeping their jobs may well hinge on how they vote on a series of contentious issues in the course of the trial -- with whether or not witnesses should be allowed to testify right at the top of that list.

And those five are joined by the likes of, among others, Sens. Lisa Murkowski (Alaska), Mitt Romney (Utah) and Lamar Alexander (Tennessee) who have all voiced support -- or the possibility of support -- for witnesses in the Senate trial. So that's eight (at least) potential Republican defectors on the witnesses vote, which should concern McConnell, given that the 47 Democrats only need to convince half that number to side with them in order for there to be witnesses called.

Now, the devil could be in the details here, of course. Public support for "new" witnesses is vague. Who wouldn't support the idea that witnesses with new information pertaining to a trial should be called, after all? The issue could come when we get down to the specific witnesses each side wants called. It's very hard for me to imagine that Republicans would allow former national security adviser John Bolton to be deposed without demanding a preferred witness of their own -- like, say, Hunter Biden, the son of the former vice president. What would the public -- especially Republicans -- make of that sort of tradeoff? Would 7 in 10 still support it?

That's what we don't know. And McConnell may well be banking on the idea that while a large majority of Americans (including almost half of Republicans) support the general idea of witnesses, when specific witnesses are discussed that support will drop considerably.

Maybe! But at the moment, the witness vote is where McConnell's plan to move this all along as quickly (and news-lessly) as possible is at its weakest. And it's where we all should be watching very closely.