The United States may have avoided a government shutdown on Saturday -- but the lack of additional funding for Ukraine in the spending bill has left some residents in the war-torn nation nervous.

Though US President Joe Biden lauded the deal reached by lawmakers, he also acknowledged the lack of new funding for Ukraine, vowing Washington "will not walk away" from Kyiv. Meanwhile, a bipartisan group of leaders in the US Senate also promised to vote on more aid for Ukraine.

For some in the Ukrainian capital Kyiv, the drama that has engulfed Congress for the past week is little more than noise as the war rages on.

"These are internal American games. And Ukraine is a hostage to this discussion -- this internal war," Ukrainian serviceman Volodymyr Kostiak told CNN on Sunday, a national holiday marking Defenders Day to honor the country's veterans and war dead.

"America's strategic interests are so big that Ukraine is part of them," he added. "And I think that the internal political struggle cannot affect the assistance to Ukraine that much. There will be some errors, but they will be insignificant."

Kostiak said the fight over funding Ukraine is due to the political realities of the 2024 US presidential election, but he believes the possibility that Washington would stop helping Ukraine is slim.

"The US budget has been suspended 20 times in history, and never once has it led to any serious consequences," the serviceman said. "So I don't see this as a big problem for Ukraine."

Natalia and Serhii Krasnoshchoks, an English teacher and an entrepreneur, were similarly optimistic.

"Yes, we have seen the news, but we think that there will be aid to Ukraine anyway," they said. "We hope so very much. And of course, we will be grateful for any help. The more, the better."

Mykhailo Chendei, a store administrator, told CNN he believed it would be "impossible" for the US to withdraw aid entirely -- but "now it's an internal American issue."

Others in the Ukrainian capital were less confident however -- especially as American support wanes, nearly 20 months into the war.

A CNN poll in August found that most Americans oppose Congress authorizing additional funding to support Ukraine in its fight, with the public roughly split on whether the US has already done enough.

It shows a shift in public enthusiasm, with a similar poll conducted in the early days of the invasion, in February 2022, finding that 62% of people surveyed felt the US should have been doing more.

Partisan divisions have widened since that poll, too, with most Democrats and Republicans now on opposing sides of questions on the US role in Ukraine.

Jeffrey Sonnenfeld, a professor and senior associate dean for leadership studies at the Yale School of Management, said Russian President Vladimir Putin would be closely watching the 2024 US presidential election as his invasion of Ukraine falters.

Putin is "hoping that by January 2025 that [former president Donald] Trump is back in there, and that will see a weakening of the resolve of the allies," Sonnenfeld said.

But "there is no weakened resolve" in Congress, he added. "It's just silly politics here that carve things up into pieces," Sonnenfeld said.

'Difficult consequences for everyone'

The US budget currently includes about $1.6 billion for the defense industry and $1.23 billion for direct budget support, as well as funds for humanitarian and energy projects, Ukraine's Foreign Ministry said Sunday.

In a Facebook post, ministry spokesperson Oleg Nikolenko said Kyiv is working with its partners in Washington to ensure that the budget Congress will work on over the next 45 days will include new funds to help Ukraine push back against Russia.

Ukrainian President Volodymyr Zelensky, who traveled to the Capitol last month to ask for more relief, has previously warned that a drop in US support could have severe consequences for the war effort.

"Of course we are alarmed [by the lack in additional funding], because for us this war is literally daily reality," Ukrainian Parliament member Inna Sovsun told CNN on Sunday. She described waking up at 4 a.m. that day because of air raid alarms, and taking shelter with her son in a bathroom away from windows in case of a missile blast.

"I understand that the US has its own political reality, it has common elections, and it has become part of the political process there," she added. "I just want the US to remember that there is a human cost to all of that, and that all those delays ... come at the cost of life."

Back on the streets of Kyiv, logistician Tetiana Ostapchuk said Sunday she hadn't heard much about the stopgap spending bill but added: "I can say for sure that we really need support from other countries, because we can't do it alone."

"Aid is very important. If it suddenly happens that America will no longer help us, then we will all fight to keep our land free. To the last man," she said. "But it would still be easier with aid."

Yulia Mueller, a chief accountant, also offered a grim prediction. "There may be a situation where the aid will stop, because a large percentage of Americans are unhappy that their money is being sent to Ukraine, that Ukraine is far away, that there is no threat to the US," she said.

"On the other hand, it seems to me that all sane people who see the atrocities that have been and are happening here now -- how entire cities are being wiped out -- understand that this can spread to other countries as well," she added.

"If America stops helping us, there will be very difficult consequences for everyone."