As talks progressed Wednesday on a compromise border security amendment, Senate negotiators appeared to have hit a crucial sticking point that, if not resolved, could undercut the viability of the "Gang of Eight" immigration-reform package.

Republicans who could support the overall bill but who are unhappy with its current border security provisions want Congress to spell out an enforcement strategy that the White House would have to follow. Failure to follow Congress' mandate could delay the legislation's plan to provide a pathway to citizenship for 11 million illegal immigrants.

Democrats are on board with the plan. So far, so good.

Republicans also want to require the construction of a fence along portions of the U.S.-Mexico border and other security improvements.

Democrats are on board with this as well. Again, so far, so good.

Also on the Republicans' list of priorities is a provision that would leave it to Congress, rather than the executive branch, to determine when the border is adequately secured and illegal immigration sufficiently reduced so that the citizenship process could proceed.

On this, the GOP and Democratic negotiators parted company. By late Wednesday, they were still without an agreement.

Democrats fear that allowing Congress to decide when the border is fully secure would delay indefinitely the pathway to citizenship that is the Democrats' top priority.

"It comes down to, what steps do you take to secure the border and then how do you measure it? And getting agreement on it. Because those become the triggers to getting to a Green Card," said Sen. John Hoeven, R-N.D., who along with Sen. Bob Corker, R-Tenn., is the principle author of the compromise amendment.

Hoeven and Corker are pushing Democrats to accept, among other measures, a provision that would require border enforcement agents to arrest or turn back "at least 90 percent" of the immigrants trying to get into the U.S. illegally.

With the nonpartisan Congressional Budget Office predicting that the Senate legislation would only reduce illegal immigration by 25 percent, Corker and Hoeven believe their hand is strengthened, particularly since the “Gang of Eight” promised their bill would halt future illegal crossings.

The Corker-Hoeven amendment also reflects the kind of changes that Sen. Marco Rubio, R-Fla., indicated would have to be made would have to be made before he’ll support the overall bill that he helped draft in the “Gang of Eight.”

Republican and Democratic negotiators appeared mildly optimistic that they could reach an agreement on the changes. But while Democrats remained tight-lipped about the negotiations that they said were at a sensitive stage,

Hoeven publicly revealed Democrat’s chief position in the talks.

“They’re pushing back and saying: ‘Well, we’re not sure when we could attain’” some mandated level of border security, Hoeven said. “So, what they’d rather do is add border security personnel and add fencing and a number of other things — instead — to get to the Green Card. And, so that’s where we’re kind of going back and forth and we don’t have agreement yet.”

Will the two sides reach a deal? This is what Sen. Charles Schumer, D-N.Y., a member of the “Gang of Eight,” had to say:

“We’re working. We’re having good, productive discussions, but you never know.”