President Biden appears to be inching closer to a deal on the southern border as the emergency spending bill to provide billions of dollars in new security assistance for Ukraine and Israel was blocked in the Senate on Wednesday.

As Senate Republicans blocked the advance of tens of billions of dollars in military and economic assistance for Ukraine Wednesday, President Biden berated their tactics as “stunning” and dangerous. Yet he also signaled an openness to what GOP lawmakers ultimately want — tougher action on the border.

The vote was 49 in favor to 51 against, leaving the $110.5 billion measure short of the 60 votes needed in the Senate to pave the way to start debate, threatening President Biden’s push to provide new aid before the end of 2023.

The bill would provide about $50 billion in new security assistance for Ukraine, as well as money for humanitarian and economic aid for the government in Kyiv, plus $14 billion for Israel as it battles Hamas in Gaza.

At the White House, Mr. Biden warned of dire consequences for Kyiv — and a “gift” to Russia’s Vladimir Putin – if Congress fails to pass a package of wartime funding for Ukraine and Israel as well as other national security priorities. Hours later, Senate Republicans defiantly voted to stop the package from advancing, something that they had threatened to do all week.

Yet even as he lashed Republicans for their stance, Mr. Biden stressed that he is willing to “make significant compromises on the border,” if that’s what it takes to get the package through Congress.

“If we don’t support Ukraine, what is the rest of the world going to do?” Mr. Biden added.

The president’s remarks Wednesday were his clearest overture yet to Republicans and came at a critical time, with a path through Congress for the emergency funds rapidly disappearing and America’s support for multiple allies in doubt. The statement has raised at least some hope that progress can be made in the days ahead.

The president’s statement came hours after he huddled virtually with Ukraine’s President Zelensky and leaders of the Group of Seven advanced democracies, which have staunchly supported Ukraine against Russia’s invasion.

“We need to fix the broken border system. It is broken,”Mr. Biden said, adding that he’s ”ready to change policy as well.” He did not name specific policy proposals and accused Republicans of wanting a political issue more than bipartisan compromise.

Senator Lankford, the Oklahoma Republican who has been leading Senate negotiations over border policy, was encouraged by what he heard, saying it seemed like the president is “ready to be able to sit down and talk.”

Senators of both parties acknowledged they will need to move quickly if a deal is to be struck. Congress is scheduled to be in Washington for just a handful more days before the end of the year. The White House, meanwhile, has sounded the alarm about what would happen if they don’t approve more funding soon, saying Ukraine’s military would be stalled, or even overrun.

Democrats involved in the negotiations also said a direct hand from the president, as well as from the Republican leader, Senator McConnell, could be helpful.

So far, Mr. McConnell, while an ardent supporter of Ukraine aid, has sided with Republicans who are holding firm against the security package unless it includes changes to America’s border policies. Every Republican voted against it advancing Wednesday evening.

Senator Schumer also voted “no” so that he could introduce the measure again in the future. “He urged Republicans to present a border proposal that is “serious, instead of the extreme policies they have presented thus far.”

Republican negotiators are expected to send a new proposal to Democrats after the failed vote. Republicans argue the record numbers of migrants crossing the southern border pose a security threat because border authorities cannot adequately screen them. They also say they cannot justify to their constituents sending billions of dollars to other countries while failing to address the border at home.

So far, senators have found agreement on raising the initial standard for migrants to enter the asylum system. But they’ve been at odds over placing limitations on humanitarian parole, a program that allows the executive branch to temporarily admit migrants without action from Congress.

Senator Cornyn, a Texas Republican, said the Senate talks were “never going to be able to negotiate the kind of meaningful substantive policy changes” that Republicans want. He called Biden’s remarks “positive” and said the negotiations should next include the president, Mr. McConnell, and Speaker Johnson.

Even if the president and senators somehow find a way forward on border security, any agreement could face significant obstacles in the House. Conservatives, who have a strong hand in the closely divided chamber have vowed to block a deal unless it tacks to a broad set of forceful border and immigration policies.

Mr. Johnson, who as speaker has already expressed deep skepticism of funding for Ukraine, has  signaled he won’t support the aid package if it does not adhere to H.R. 2, a bill that would remake the American immigration system with conservative priorities. “The American people deserve nothing less,” Mr. Johnson said in a statement.