The Senate will hold a revote this week on a major border security bill months after it was blocked by a bipartisan filibuster, with Democrats saying they hope to embarrass Republicans into switching their stance and embracing the legislation.

Majority Leader Charles E. Schumer announced the vote in a letter to colleagues Sunday evening, hoping to gain some political traction on an issue that has become a major problem for President Biden and congressional Democrats.

The bill includes some new powers to block migrants at the border and expands the capacity to detain immigrants who are in the country illegally rather than release them, albeit with significant limitations and carveouts. It also changes asylum standards to help block bogus claims earlier in the process.

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It was attached to a broader bill with U.S. military assistance for Ukraine and Israel. The measure fell victim to a bipartisan filibuster, garnering just 49 votes of support — well shy of the 60 needed to surmount the filibuster. Nearly all Republicans voted against it, as did a handful of Democrats.

Mr. Schumer said Republicans spent years complaining about the border, then defected once they were presented with a solution. He blamed former President Donald Trump for the reversal, saying Republicans’ presumptive presidential nominee didn’t want to see something that would solve the border for Mr. Biden.

“The former President made clear he would rather preserve the issue for his campaign than solve the issue in a bipartisan fashion. On cue, many of our Republican colleagues abruptly reversed course on their prior support, announcing their new-found opposition to the bipartisan proposal,” Mr. Schumer said in his letter Sunday.

But House Republicans had already made clear they would reject the bill even before Mr. Trump’s opposition. They said the measure didn’t come close to the kinds of changes they wanted to see to stop what’s become the most chaotic border in modern history.

That GOP opposition hasn’t changed; Mr. Schumer’s revote is unlikely to fare any better.

What Democrats want the revote to do, however, is to rewrite the tricky politics of immigration. Mr. Schumer said voters should see Democrats as the party trying to solve the problem.

“At the end of the day, the American people deserve political leaders who will work towards bipartisan solutions and that is what we are prepared to do in the United States Senate this coming week,” he wrote.

The bill was negotiated over months, with the details kept largely secret. During that time Republicans had sounded optimistic while Democrats expressed worry.

When the deal was finally made public in February it was Republicans who were dismayed with the details.

They said the changes might shift the demographics of who’s coming, but they doubted the overall numbers would dip much, which they said undercut the reasons for the bill in the first place.

“We have no confidence — zero confidence — that the Biden administration will enforce the law when it comes to the border,” said Sen. John Cornyn, Texas Republican, at the time.

The irony is that in the months since, border numbers have dipped. Analysts say it’s largely because Mexico has gotten more serious about its own enforcement, interdicting migrants before they reach the U.S.

In April, the Border Patrol caught 128,884 immigrants crossing the southern border illegally. That’s the third-best month since Mr. Biden took office. But it’s still worse than all but one month under Mr. Trump.

And while the Border Patrol numbers are down, overall levels of unauthorized migration are still setting records, thanks to several “parole” programs invented by the Biden administration. Those programs allow quick catch-and-release for migrants, even though they lack visas, as long as they pre-schedule their arrivals and come through official ports of entry.

Officers at ports of entry recorded 116,771 unauthorized entries in April. In December 2020, the last full month under Mr. Trump, that figure was less than 22,000.