President Joe Biden and Donald Trump are trading blame for the stalling of a bipartisan immigration bill.
The measure has already been rejected by House Republicans and is facing mounting Senate opposition.
Mr Biden said in a White House speech that his predecessor would "rather weaponise this issue" than solve it.
Mr Trump's campaign said Biden policies were "causing death, destruction, and chaos in every American community".
Supporters - including Democrats and Republicans in Congress - argue that the 370-page bill would stem the record-setting pace of undocumented immigrants at the southern US border.
If passed, the legislation would spend hundreds of millions of dollars on border wall construction.
It would also fast-track decisions on asylum cases, limit humanitarian parole, and expand the authority to deport migrants.
The bill would allow the federal government to shut down the border when migrant crossings pass a threshold of 5,000 per week.
The $120bn (£95bn) includes about $20bn of US border funding, $60bn to support Ukraine in its war against Russia, and another $14bn in security assistance for Israel.
On Tuesday evening, House Republicans tried spinning off the Israel aid into its own $17.6bn (£14bn) package, but it failed to pass.
The party's lawmakers also narrowly failed to impeach Mr Biden's top immigration official, the homeland security secretary, over the border crisis.
"The world is watching," Mr Biden said at the White House earlier in the day. "They are waiting and watching what we're going to do. We can't continue petty partisan politics."
Still, the president conceded that "all indications are this bill won't even move forward to the Senate floor", despite the support of the Border Patrol Union.
"Why?" he asked. "A simple reason: Donald Trump. Because Donald Trump thinks it's bad for him politically."
Mr Biden said the former president had spent the past 24 hours lobbying Republicans in the House and Senate in an effort to torpedo the proposal.
He said Mr Trump had tried to intimidate Republican lawmakers, "and it looks like they're caving".
Mr Biden urged the lawmakers to "show some spine".
The Trump campaign blasted the Biden speech, calling it "an embarrassment to our Nation and a slap in the face to the American people".
Spokeswoman Karoline Leavitt called Mr Biden's criticism of Mr Trump "a brazen, pathetic lie and the American people know the truth".
Her statement also said Mr Trump's policies had "created the most secure border in American history, and it was Joe Biden who reversed them".
On Monday, Mr Trump posted on social media that "only a fool, or a radical left Democrat" would vote for the bill.
Even if the bill were to pass the Senate, which is expected to vote on Wednesday, it looks likely to flounder in the House. Speaker Mike Johnson has already vowed it would be "dead on arrival".
The deal has also drawn the ire of immigration activists, who say the Biden administration is not meeting its campaign promises.
Erika Pinheiro, executive director of Al Otro Lado, a group that provides legal and humanitarian support to migrants, said: "The Democratic party has completely abandoned the pretence of caring about immigrants because they think it will help them in the next election."