"He is eager to go down to Texas and show his support," Psaki told ABC News Chief Washington Correspondent Jonathan Karl on "This Week." "But he's also very mindful of the fact that it's not a light footprint for a president to travel to a disaster area. He does not want to take away resources or attention."
Biden approved a major disaster declaration for Texas on Saturday, opening up federal funds to 77 of the state's 254 counties, yet Gov. Greg Abbott originally asked for a declaration for the entire state. After the declaration was announced, Abbott said the "partial approval is an important first step."
Karl asked Psaki if the president and governor have spoken about his request that the whole state receive the major disaster declaration.
"Are they on the same page now about this?" Karl asked.
She said that the White House has been in "close touch" with Abbott and that Biden is getting regular updates from his team.
"What happens here is the governor requested a federal disaster declaration, the president asked his team to expedite that and FEMA determined where the counties should be, where it should focus the immediate resources, where the counties that are hardest hit, so that they can make sure they get the people in most need," Psaki said.
The severe weather across the country has also created havoc on distributing the COVID-19 vaccine to all 50 states, delaying 6 million doses. The weather kept employees along the distribution line from getting to work, delivery drivers off the road and -- most acutely -- shut off the power for thousands of vaccine sites, White House senior adviser Andy Slavitt said on Friday. He also said the packaging plant for Moderna vaccines was also just coming online.
But Psaki told Karl on Sunday that help is on the way.
"We've been able to get about 2 million of those 6 million doses out, we expect to rapidly catch up this week, fill that backlog, make sure they're out to communities, and also meet our deadlines and our timelines of the doses that are due to go out this upcoming week."
Vaccinating the nation's students and getting them safely back into a classroom has also come to be a challenge for the Biden administration. The president originally promised to reopen all schools within his first 100 days, but then shifted that goal to just kindergarten through 8th graders.
Two-thirds of the country is still categorized under the Centers for Disease Control and Prevention's "red zone," which means those school districts are encouraged to continue hybrid/virtual learning unless every mitigation effort is followed.
But Psaki said the president remains unwavering in his commitment to meet his mark and see them return to class.
"That's our goal. That's our objective. That's our plan," she said.
Psaki said schools need more funding if they want to reopen in that timeframe, which is why she says Biden has proposed additional aid for them in his $1.9 trillion COVID-19 relief bill.
"What we need -- and what the president said at the time -- we need his funding," she said. "That's why he's proposed $130 billion dollars in the American Rescue Plan because many schools across the country don't have the resources to be able to invest in improving facilities on hiring more bus drivers on hiring more temporary teachers so we can have smaller class sizes."
Karl asked if Biden wants to make that funding contingent on schools actually reopening, Psaki said that that is not currently being discussed.
"That's not a contingency that we're putting in -- we're recommending to go in -- in the bill or in legislation," she said.
The House Budget Committee is expected to "markup," or debate, review and amend, the bill on Monday and the full House is expected to pass the bill by the end of next week before it goes to the Senate.
Biden's plan has no Republican support, despite the president saying he would get Republicans on board. He also faces a hard sell to two Democrats, Sens. Joe Manchin and Kyrsten Sinema, over the minimum wage hike in the package.
CDC Director Rochelle Walensky said earlier this month that increasing data shows that schools can safely reopen "and that safe reopening does not suggest that teachers need to be vaccinated."
Despite that, some teachers unions, such as the California Teachers Association, have come out against schools reopening until every educator is vaccinated.
Karl pressed Psaki on Sunday if Biden and Vice President Kamala Harris believe all teachers should be vaccinated for schools to reopen, Psaki repeated the administration's go-to line of only saying they should be "prioritized."
"The vice president and the president and the federal government, we all believe that teachers should be prioritized. And now about half of the states in the country also have prioritized teachers and they put them in the priority or the priority category of frontline health care workers because of the role that they play, but it doesn't need to be a prerequisite. … Our science experts are saying it's not a prerequisite and that's the guidelines that we follow."
Some states, including New Hampshire and Iowa are mandating local districts reopen schools over the next few weeks. Democratic governors in Minnesota and Virginia are also calling for schools to start reopening in the next few weeks. When asked if the White House approves of these mandates, Psaki avoided directly answering, only saying that's not a decision made by the federal government.
"The role we're playing from the federal level is to support the CDC guidelines science based guidelines that are giving school districts, the roadmap they need to reopen, but these decisions are not made by the federal government, they're made by states, they're made by local school districts and we certainly respect that."
While Psaki reiterated that many aspects of the coronavirus response are ultimately left to local leaders, New York Gov. Andrew Cuomo, who Biden praised early on for his leadership during the pandemic, is now under fire related to some of his decisions early in the pandemic.
It was revealed last week that the FBI and a U.S. attorney are investigating the governor's coronavirus task force, with a particular focus on his administration's handling of nursing homes early in the coronavirus pandemic. New York Assemblyman Ron Kim has also detailed what he described as a "threatening" exchange he had with Cuomo after speaking out.
Karl played a clip of Biden saying the governor had done "one hell of a job," and asked Psaki if Biden still stands by his praise that Cuomo represents a "gold standard."
"Well, Jon, we work with Gov. Cuomo just like we work with governors across the country," she said dodging a direct answer.
"We're going to continue to work with a range of governors including, of course, Gov. Cuomo because we think the people of New York, the people of states across the country, need assistance not just to get through the pandemic but to get through this difficult economic time, and that's where our focus remains."
Pressed a second time by Karl for a "yes or no" to his question, Psaki again avoided directly answering and said she didn't want to appear to "give new labels or names from the president."
"It doesn't always have to be a yes or no answer, Jon. I think the president is focused on his goal, his objectives as president of the United States. He's going to continue to work with Gov. Cuomo just like he'll continue to work with governors across the country."
ABC News' Cheyenne Haslett contributed to this report.