Senate Democrats have privately decided that the amendment offered by Senator John Cornyn to strengthen border security — the latest high-profile effort by Republicans to shift the bill dramatically to the right — is too onerous and is unacceptable to them, according to an aide to a Democratic member of the Gang of Eight.

The move is important, because Cornyn’s amendment has emerged as a key new demand among Republicans as part of their effort to make the bill acceptable to conservatives — which ultimately can be seen as a challenge to determine just how much Dems are willing to give away to get broad support for the bill. If Dems stick to their vow to kill the Cornyn amendment, it will send an encouraging sign that Dems really do intend to hold the line against any Republican efforts to undermine the core of the bill, i.e., the path to citizenship.

Senate Dems have decided that two key aspects of Cornyn’s amendment — which are designed to create enforcement “triggers” that must be met before the path to citizenship is operative — are unacceptable, the aide tells me. In particular, Cornyn’s demand for at least a 90 percent apprehension rate along the southern border, and the “Biometric Exit System” being fully operational at all air and sea ports of entry, are both unacceptable as triggers for citizenship, the aide tells me.

As for Cornyn’s demand that the bill provide for the hiring of 5,000 border security agents, the Dem aide notes that Republicans have not explained how this would be paid for, so the idea is unworkable on its face. (This echoes some of David Drucker’s recent reporting.)

This is a key marker from Dems. It is intended to send a signal to Republicans that they are not willing to allow them to undermine the most basic aspect of the bill — that the path to citizenship not be contingent on unreasonable demands or triggers. It complicates matters for Marco Rubio, a member of the bipartisan Gang of Eight, who is trying to demonstrate that he is pushing the bill to the right — and has said he is broadly supportive of Cornyn’s efforts as part of that process.

All of this comes as Senate Democrats are preparing for a bruising few weeks, in which Republicans are expected to offer a series of new amendments designed to move the bill to the right (or, in some cases, to kill it outright). Advocates on both sides are trying to determine how hard a line Dems are genuinely willing to draw.

Some aides have fastened on to Chuck Schumer’s suggestion on the Sunday shows that Dems should try for 70 votes in the Senate in order to project broad bipartisan support, in hopes that this will force the House GOP to act. Some worry that setting this goal projects a willingness up front to make concessions and could put Dems in a weaker position later, and ask whether the vote total in the Senate will even make a difference to the House GOP, given the enormous hostility among Republicans toward reform.

“If the House passes anything, it’s likely to be a very bad bill and we’ll have to go to conference with our bill and their bill, so our bill should be the strongest possible starting point for those negotiations,” one senior Senate Dem aide tells me. “We will put enormous pressure on Speaker Boehner simply by passing a bill. Passing it by 70-plus votes would be a nice cherry on top but it’s not worth giving away major concessions to get it.”

The flip side of this argument is that it may be a false choice. Perhaps Schumer is merely making a prediction that it can win 70 votes, not arguing that Dems should give a lot away to achieve them. In any case, the bill is going to be changed throughout the amendment process, and some amendments strengthening border security — provided they don’t undermine the path to citizenship — might be desirable, since it could give Republicans a way to say to conservatives that they achieved border security concessions for them. In this sense, Dems are engaged in a very delicate dance, in which they need to signal that they will not give an inch on anything that undermines the path to citizenship, even as they do permit the process to give Republicans a way to argue to conservatives that their interests are being advanced.

Also, it’s very possible that House Republicans won’t pass anything, and that there will be no conference negotiations. If that happens, the question will be whether House GOP leaders are willing to allow a vote on the Senate bill — perhaps even letting it pass with mostly Dem votes. That could perhaps be more likely if the Senate bill passes with broad support (though that’s not clear).

If Dems hold fast against Cornyn’s amendment, an important message — that anything that compromises the path to citizenship is unacceptable — will be loud and clear. And it will mean that immigration reform’s prospects turn on one thing, and one thing alone: Can Republicans accept a path to citizenship with reasonable conditions, or not?