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If Pence were so inclined, he literally/physically could do what Rasmussen says here, but in the end this gambit would fail. How so? Let's see.
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But first: Despite what Rasmussen says, the power of the President of the Senate at the counting of the electoral votes is NOT "plenary and unappealable". Indeed, if you look closely, you'll see the Constitution doesn't say he presides, just that he opens the envelopes.
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In short: This is not the President of the Senate's Show; it's Congress' show and in the end they decide.
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Now, the step-by-step.
Rasmussen claims the Constitution grants Pence the "authority" to do whatever he wants, including refusing to open certificates from states on Trump's naughty list. Yet that same Constitution (12A) requires him to open "all" of the certificates. So…
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Rasmussen claims the Constitution grants Pence the "authority" to do whatever he wants, including refusing to open certificates from states on Trump's naughty list. Yet that same Constitution (12A) requires him to open "all" of the certificates. So…
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Recall the process: The VP opens the states' certificates in alphabetical order. As he opens each one, he hands it to the tellers to count, who ascertain that it's "regular in form and authentic" and count it, then one teller announces that state's votes for POTUS and VPOTUS.
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So what would happen if, as Rasmussen says could happen, Pence actually skipped over a state and handed the next in alphabetical order state's certificates to the tellers?
Can't say for sure, but...
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Can't say for sure, but...
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Here's how I envision things rolling: A House or Senate member would object that the skipped state's certificate should not have been skipped & then as required by the rules, the objection would quickly be put to paper & signed by at least 1 member of the House and Senate.
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But what if Pence wrongly ruled that objection out of order? I'd anticipate the tellers would refuse to continue their duties of ascertaining and counting, which in turn would stop the process.
But then if Pence tried finishing the count on his own?
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But then if Pence tried finishing the count on his own?
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Unless Pence already had literal possession of all the states' certificates, I figure the House clerk, at the direction of the Speaker, would refuse to hand Pence the remaining ones, and so THAT would stop the process.
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But after all that, what if Pence persisted? The Speaker could order the cameras, mics & lights turned off and the House Sergeant at Arms to clear the chamber (at least of all House members) – it is her chamber, after all – and thereby would end the "presence" of the House.
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Yes, that scenario things end with all the subtlety of the crash-the-set scene at the end of Blazing Saddles...
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Anyways, what I've attempted to show in this thread is how things might actually roll irl – vs how con law experts are saying things should roll – if Pence did decide to go rogue... because why game things out per the rules if the premise is Pence ignoring the rules? 
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Okay, so what would happen next? I think this could work (corrections welcome)…
1) The House & Senate could refuse to show up for continuation of the Joint Session.
2) In the AM of Jan 20, the House elects Joe Biden Speaker.
3) At noon on Jan 20 he becomes acting-POTUS.
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1) The House & Senate could refuse to show up for continuation of the Joint Session.
2) In the AM of Jan 20, the House elects Joe Biden Speaker.
3) At noon on Jan 20 he becomes acting-POTUS.
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4) On the afternoon of Jan 20, the House & Senate reconvene the Joint Session at which (b/c there's no VP) the Senate's President pro tem opens the remaining states' certificates, the tellers tally them, and then the PPT announces "the state of the vote".
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5) And with that, Joe Biden then (re)takes the presidential oath of office and Kamala Harris takes the VP's oath of office – Fin.
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