Hours after the Obama administration requested $3.7 billion in emergency funding to address the current child immigration crisis at the southern border, few on Capitol Hill were predicting speedy passage — if at all — of legislation to provide Obama with the money he has requested.

Instead, the conventional wisdom on the Hill among both Democrats and Republicans is the same as it has been for any number of issues this year — from minimum wage, to unemployment extension, to any number of jobs bills: probably not going to happen.

"No, given the mood here in Washington, I don't have confidence it will happen," said Sen. Marco Rubio (R-Fla.) on Tuesday.

Describing Obama's request as a "blank check," several top Republicans slammed the proposal. In interviews and statements issued Tuesday, GOP House members — the chief obstacle to any Obama proposal — signaled that they are unlikely to go along with this funding proposal, which is a sizable ask for funding on one of the nation's most divisive political issue that comes just months before the midterm elections.

“President Obama created this disaster at our southern border and now he is asking to use billions of taxpayer dollars without accountability or a plan in place to actually stop the border crisis," declared Rep. Bob Goodlatte (R-Va.), the House Judiciary Committee chairman, in a statement. "President Obama has many tools at his disposal now to quell this activity at our southern border, such as enforcing immigration laws and cracking down on rampant asylum fraud. Unfortunately, none of these tools are mentioned in his proposal."

The leadership of both the Republican and Democratic caucuses spoke cautiously Tuesday of the White House proposal, with many top members saying they had yet to read the full details. But both sides also expressed reservations.

“The Appropriations Committee and other Members, including the working group on the border crisis led by Rep. Kay Granger, will review the White House proposal," said Michael Steel, a spokesman for House Speaker John A. Boehner (R-Ohio), in a statement. "The Speaker still supports deploying the National Guard to provide humanitarian support in the affected areas — which this proposal does not address.”

A non-starter for many congressional Republicans was the decision by Obama to not request a congressional change to the 2008 law regarding how children caught illegally crossing the border are treated. Children from Mexico can be immediately sent back, but children from countries that do not directly share a border with the U.S. — such as Honduras, El Salvador and Guatemala, where many of the immigrants causing the current crisis hail from — must be afforded greater legal rights and be held for longer.

"The important thing is to expedite this process and not to require that HHS place these kids," said Sen. Jeff Flake (R-Ariz.). "Nothing will stop the flow like seeing a plane come back with kids and for people to realize that they just spent $5,000 to $7,000 to cross the border and now they're back. I'm telling ya, if you want to solve the problem, that'll do it.”

Sen. Lindsey Graham (R-S.C.) also said that the key is to alter the law.

"This is truly an emergency. You (need to) create a deportation process based on the situation we face," said Graham, who was one of several Republicans pushing for comprehensive immigration reform in the Senate. "I just think the average American will say that if you don't deport these children, others are going to keep coming. The 2008 law was not designed to address this situation. ... I think you take the 2008 law and you ... come up with a law that will address this situation."

Even if the Republican lawmakers are willing to support the content of the Obama funding request, it remains to be seen whether they will insist that the funding be offset — which could doom the legislation.

"We don't have any room within the appropriations budget for any offsets," said Sen. Richard Durbin, (D-Ill.), who added that, while he had yet to read the full proposal from the White House, there were also concern among Democrats about whether the Obama administration's proposals were the best way to solve the crisis.

"This is a heartbreaking moral crisis for this country. We are dealing with children stacked up in holding cells overnight for two, three days at a time," Durbin said. "This is our test, and I hope we handle it in a way that we can look back at this with some pride."

Durbin, a member of the Democratic leadership, said that several members of his caucus have expressed concerns about reforms to the legal processes for the children who are caught attempting to cross the border illegally.

Durbin described the Obama proposals as three-tiered: a request for more money, new penalties for human traffickers and revisions to the legal process faced by children caught sneaking into the country.

"The third one ... is the one where a lot of us have questions; I haven't seen any detailed language." Durbin said. "I just want to make sure that at the end of the day we're being fair, human and doing this in an orderly way."

Still, several top Democrats have rallied around the Obama proposal.

"I commend the Administration for doing what it can to quickly address this surge of children and families attempting to enter our country, and I urge my colleagues in Congress to support it," said Sen. Tom Carper (D-Del.), who chairs the Homeland Security and Governmental Affairs Committee, in a statement.

The rift between the parties hinges on a fundamental disagreement in how the current crisis can be best handled. Republicans argue that Obama must stop the flow of illegal immigrants to the border and ensure that the entire border is secure before focusing on the tens of thousands who are already in detention facilities there.

"You are never going to pass anything else on immigration until you deal with the enforcement first. Period," Rubio said.

Citing that logic, Heritage Action, the Super PAC associated with the influential conservative think tank that closely monitors how Republican lawmakers vote, decried the Obama funding proposal as a "non-starter."

“President Obama’s request is a non-starter because it seeks to address the symptoms, not the cause," Michael A. Needham, Heritage Action's CEO, said in a statement. "The President should rescind his anti-enforcement policies and demonstrate a commitment to implementing existing law."

Democrats, meanwhile, say that the first step must be to provide more funding to pay for new detention facilities and legal services to work through the debilitating backlog of children who are already at the border.

Providing an influx of money for detention centers and to pay for additional judges, several Democrats have argued, is more urgent than altering the 2008 law in terms of addressing the current crisis.

“The process I don’t think is the problem," said Sen. Dianne Feinstein (D-Calif.). "I think it is a real crisis. Lives are going to be lost and mistakes are going to be made, so I think this supplemental is really all important to get passed.”

Meanwhile, other Republicans have continued to hammer Obama for his plans to attend a series of Texas fundraisers later this week and not visit the border while he is in the state.

"If it's serious enough for him to send a $3.7 billion funding request to us, I would think it would be serious enough for him to take an hour of his time on Air Force One to go down and see for himself what the conditions are," Sen. John Cornyn (R-Tex.) told reporters after declining to comment on the funding request, which he said he had yet to read. "I think it would be instructive for him."

— Ed O'Keefe contributed to this report.