By Caroline Kelly, CNN

(CNN) -- House Speaker Nancy Pelosi on Tuesday slammed the White House's most recent stimulus proposal as ignoring key economic issues wrought by the coronavirus pandemic, defending her decision to turn down what she described as a political stunt that would fail to help the public.

"All of my colleagues -- we represent these people, I have for over 30 years represented my constituents," Pelosi told CNN's Wolf Blitzer on "The Situation Room." "I know what their needs are, I listen to them, and their needs are not addressed in the President's proposal."

When asked whether she could avoid letting the perfect be the enemy of the good, Pelosi replied, "I will not let the wrong be the enemy of the right."

Pelosi's comments come after Majority Leader Mitch McConnell announced Senate Republicans will attempt to move forward on a "targeted" coronavirus relief bill when the Senate returns to session next week -- a sign that prospects for broad stimulus agreement have all but faded before Election Day.

Despite the urgency expressed throughout the country, the negotiations have only appeared to get further away from a resolution in recent days -- and significantly more confusing. While President Donald Trump offered a momentary boost to the prospects of an agreement last week when he called for a "big" deal and proposed a $1.8 trillion offer, Pelosi has rejected the effort as insufficient on several major fronts and the talks are once again stuck without a clear path forward.

Pelosi dismissed Blitzer's references to other Democrats calling for a relief bill -- such as California Rep. Ro Khanna warning that people can not wait for aid until February, former Democratic presidential candidate Andrew Yang saying that there was some good in the Republicans' offer and the Problem Solvers Caucus' proposal.

While the two men are "lovely," Pelosi said, "they know nothing about" the specifics of the White House's proposals and "they are not negotiating this situation -- they have no idea of the particulars, they have no idea of what the language is here."

Members of the Problem Solvers Caucus "don't have any earned income tax credit or child tax credit in their proposal, either," like the White House proposal, she added.

"With all due respect to the kind of people you were referencing -- and I welcome their enthusiasm, I welcome their interests, I welcome their originality of their thinking," Pelosi said. "But the fact is we have a responsibility to meet the needs of the American people in a retroactive way so they are not at a total loss."

"Nobody is waiting until February -- I want this very much now, because people need help now," Pelosi said. "But it's no use giving them a false thing just because the President wants to put a check with his name on it in the mail that we should not be doing all we can to help people pay the rent, put food on the table and enhance benefits."

Asked to respond to Pelosi's comments, Khanna told CNN's Poppy Harlow on Wednesday that he has great admiration for the House speaker and her negotiating skills.

"I'm just talking about people I hear in my district," he said during an interview on "Newsroom." "I'm speaking for them. That's my job as a member of Congress to say we've got to help them and get something done."

He also said a lot of his fellow lawmakers want a deal but agreed that Pelosi is "right there has to be some things that need to be amended."

"We need to get the money for testing, we need a full comprehensive testing plan," he said, adding. "We should make a deal. I'm not saying we should take exactly the language of what the White House offered. What I have said is we ought to be able to -- we're close and we should be able to make the deal and I think we can."

Pelosi on Tuesday also slammed Republicans as proposing unacceptable cutting from the next stimulus agreement.

"They minimize the need for child care" and removed the child tax credit and expanded unemployment insurance "benefits to the extent that it was agreed to before," she said, criticizing their proposed "tax break for the wealthiest families in the country while they cut out the earned income tax credit for the poorest families in our country and the poorest children in our country."

Conversely, she also emphasized her committee chairs' abilities to advocate for the right stimulus elements.

"I have every confidence in the arguments we make because it's based on science and documentation," she said. "Our chairs know their stuff. They know what they are doing."

This story has been updated with additional developments Wednesday.