"We know the documents are relevant, and we know the President is desperately trying to conceal them," Ms Demings said.
Why does all this matter? The Democrats are basically arguing that the previously-obtained communications prove there is more relevant information out there. But the Republicans are actively blocking it, claiming executive privilege, on the hopes that the President will score a quick acquittal with little debate.
The Democrats need at least four Republican senators to vote to see new documents or witnesses. These numbers are possible, but so far the party remains united against it.
WHAT WAS IN THOSE TEXT MESSAGES?
During the House Democrats' impeachment inquiry, a series of text messages were released revealing communications between top Trump administration diplomats, his personal lawyer, and Ukrainian officials.
Ms Demings displayed texts between US envoy to Ukraine Kurt Volker, US diplomat Bill Taylor and Ambassador Gordon Sondland, which showed that the Trump administration's pressure campaign was presented as a quid pro quo.
Specific texts revealed Mr Trump's decision to withhold almost $400 million in military aid from Ukraine.
One State diplomat, Bill Taylor, repeatedly raised concerns that this was connected to Mr Trump's demands for the investigation.
"Are we now saying that security assistance and WH meeting are conditioned on investigations?" Taylor wrote on September 1.
"Call me," Sondland answered.
Eight days later, Taylor wrote: "As I said on the phone, I think it's crazy to withhold security assistance for help with a political campaign."
While these were only a portion of the materials — meaning they could be missing context — the texts were not a good look for the Trump administration.
Ms Demings argued that the texts and other messages uncovered by Democrats make clear there's more damaging information out there.
She said further information "would help complete our understanding of how the President's scheme unfolded in real time".
WILL THE DEMOCRATS GET THEIR NUMBERS?
The Democrats need just four Republican votes to force the Senate to subpoena witnesses and documents.
While the entire party voted against this today, three have signalled they may be open to doing so further down the track — Mitt Romney, Susan Collins and Lisa Murkowski.
Ms Collins, the Republican senator for Maine, released a statement towards the beginning of today's trial indicating she would be "open" to this later on.
This still leaves Democrats searching for a fourth vote, which explains the emphasis on those texts. They're hoping to tap into a fourth Republican senator who could decide that new materials are necessary, and tip the maths in their favour.
Last week, Senate Minority Leader Chuck Schumer said the vote remains unpredictable. "I can't predict to whether we'll have witnesses or not," he said. "At first everyone said no, McConnell seemed to rule the roost. Now we're having some people entertain it, but you don't know what's going to happen. So we're in better shape than we were a few weeks ago, but there's no certainties here at all."
SO IS TRUMP'S JOB AT RISK?
In short, no.
It takes two separate votes to remove a sitting President from the top job.
Last month the US House of Representatives, controlled by the Democrats, voted to impeach Mr Trump. The resolution passed by 228 votes to 193.
The Senate, controlled by Mr Trump's Republican Party, will now decide have the final say to determine whether he is convicted and removed from office.
But here, a minimum two-thirds of senators would have to vote to remove the President.
Republicans are in control of the Senate, with 53 senators to the Democrats' 47. For the Senate to convict Mr Trump and complete the process, 20 members of Mr Trump's own party would be required to vote against a man who is easily their best shot at another four years in government. That's not going to happen.
The Democrats believe the President needs to be held responsible for these alleged abuses of power regardless. They're also hoping it could sway undecided voters their way in the upcoming November election.
