Senators blocked two competing bills on Wednesday aimed at ending the separation of migrant families detained along the U.S-Mexico border, the latest sign that bipartisan talks in the chamber have failed to resolve the matter.

Sen. Thom Tillis Thomas (Thom) Roland TillisThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting OVERNIGHT ENERGY: EPA head questions connection of climate change to natural disasters | Pebble Mine executives eye future expansion in recorded conversations | EPA questions science linking widely used pesticide to brain damage in children Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (R-N.C.) tried to get consent to pass a Republican-only bill that would allow families to be detained together while they work their way through the U.S. court system. The measure also would increase the number of immigration judges.

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"I think it's important that people understand that we're making progress, and it's pretty important to keep the issue and this discussion active in the U.S. Congress because Congress needs to act," Tillis said.

But Sen. Mazie Hirono Mazie Keiko HironoManchin defends Supreme Court candidate Barrett: 'It's awful to bring in religion' Democrats shoot down talk of expanding Supreme Court Democrats unveil plan declaring racism a public health issue MORE (D-Hawaii) objected to the bill, calling the legislation a "partisan political stunt" that would "distract the American people from the crisis created by Donald Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's zero tolerance policy."

"To continue to enable Donald Trump to pursue his anti-immigrant agenda makes us complicit in his cruelty and injustice," she added.

Sen. Dick Durbin Richard (Dick) Joseph DurbinFeinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Grand jury charges no officers in Breonna Taylor death Democrats shoot down talk of expanding Supreme Court MORE (D-Ill.), in turn, tried to pass a bill that he said would tie together legislation from Hirono, to give unaccompanied children legal representation, with legislation from Sen. Dianne Feinstein Dianne Emiel FeinsteinFeinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Democrats shoot down talk of expanding Supreme Court Biden leads Trump by 12 points among Catholic voters: poll MORE (D-Calif.) that would broadly let families detained along the border stay together with the “presumption” that it is not in their best interest to be detained.

But Tillis, noting Durbin's measure had just been introduced, objected to the Democratic bill.

"We have not had an opportunity to study it," he said. "But without analyzing and [reconciling] it against a bill that I'm actively involved in that the senator mentioned, I object."

The stalemate on the Senate floor comes as talks between Feinstein, Durbin, Tillis and Sen. Ted Cruz Rafael (Ted) Edward CruzCruz blocks amended resolution honoring Ginsburg over language about her dying wish Trump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP MORE (R-Texas) have hit a roadblock amid deep divisions about how to handle families detained along the U.S.-Mexico border.

Negotiations appeared to get off track earlier this month over two issues crucial to any agreement: what to do about the Flores settlement, which places restrictions on how long children can be detained, and alternatives to detaining families together indefinitely.

Democrats argue that Republicans want to water down or get rid of the Flores settlement, potentially creating a scenario where children could be detained indefinitely with their parents.

Tillis on Wednesday said that's a "false" narrative, adding that Republicans were looking at potential detention of 40-60 days and hoping they could reduce it further.

"What we're trying to do is figure out a reasonable, fair way to keep families together, to have families prioritized so that they can go before a judge and determine whether or not they have a legitimate asylum claim and move as expeditiously as possible," he said.