Congressional Republicans, who have been more receptive to immigration reform since last November, now appear increasingly unlikely to widely back the Senate immigration bill unless they can extract significant concessions from Democrats.

It all comes down to the battle over border security. Some Senate Republicans are coalescing around a new border security plan as an alternative to Texas Republican Sen. John Cornyn’s, demanding acceptance of it as a condition for their support of the overall bill. But top Democrats are balking at initial drafts of their proposal and privately concede there’s little chance the Senate will add even tougher border security language to the bipartisan bill.

Failing to win significant GOP support in the Senate could imperil the bill’s chances in the House, where Republicans are already scoffing at the Senate measure. House Speaker John Boehner is vowing to put a bill on the floor only if it can win support from a Republican majority. Rather than advancing a comprehensive bill, as Democrats demand, a House committee began work Tuesday on an enforcement-only measure mainly backed by Republicans.

Congressional Republicans say the opposition from their activist base to the Senate plan is only growing, making it easier for GOP senators to oppose the Senate bill — particularly if the border security provisions remain largely unchanged.

“If you listen to the number of calls, the emails that our offices are getting right now, the bombardment is pretty one-sided,” said South Dakota Sen. John Thune, No. 3 in GOP leadership. “That’s just the way it is.”

Kentucky Sen. Rand Paul, who was once viewed as a gettable vote, said, “There’s no great groundswell of Republicans telling me to vote for this.”

The landscape could shift if Republicans are able to reach a deal quickly on border security that doesn’t turn off Democrats and if proponents can effectively sell Tuesday’s news that the Congressional Budget Office estimated the proposal would shave $175 billion off future deficits in the next decade.

Still, it was far from certain Tuesday that GOP negotiators could achieve the right balance. Top Senate Democrats are prepared to push forward with a vote even if they can’t win more than just a handful of Republicans, believing public support for the proposal will grow and that Republicans will be eager to avoid a repeat of the political fallout they suffered after the failure of the 2007 immigration bill.