A breakthrough moment for the Senate immigration bill is at hand, and it can be reduced to this formula: Two plus eight looks to equal at least 70.

The two are Republicans John Hoeven and Bob Corker, who are unveiling a plan to rewrite the border security provisions in the “gang of eight” measure in a way that will win over a solid bloc of new GOP votes without alienating any of the Democrats.

If everyone on the Democratic side embraces the deal, and if they’re joined by a third of the Republicans, the majority would crest at 70 on passage of the legislation, which sponsors are pushing for by the end of next week.

That’s the symbolically important goal set by proponents of the bill, who believe such a show of support would persuade a majority of the House’s majority Republicans to ultimately embrace similar legislation.

Speaker John A. Boehner told some Hispanic House members on Wednesday that the chamber would consider its own immigration bill this summer. At this point, though, it looks highly unlikely that most GOP caucus members are ready to vote for a path to citizenship under any circumstances, and Boehner has signaled he won’t call a vote on a bill unless he knows a majority of his troops back it.

The heart of the amendment is being dubbed the “border surge” package — authorizing more than $30 billion in the next decade to double the size of the border patrol to 40,000 agents, complete 700 miles of double fencing and other barriers astride the Mexican border, and buy a squadron of drones to see who’s still crossing the border illegally.

The government would begin granting legal status to people living in the United States unlawfully while those security enhancements were being instituted. But those immigrants wouldn’t get their permanent residency documents (green cards) until all the new people and hardware were at the border.

That sequencing is designed to be a compromise that assuages some of the GOP critics of the bill, who want tangible proof that the border has been made much less porous before allowing the people who already got into the United States illegally to start on the path to total acceptance. As put forward by the gang of eight, the legalization process would begin once the government announced a new plan for improving security, and green cards would start being issued a decade later.

Senate Minority Whip John Cornyn, a leading critic of the bill, said the border security proposal from Hoeven and Corker amounted to a “significant step forward,” but he declined to endorse the package before reading the language.

But at least one prominent group lobbying against the bill, NumbersUSA, derided the proposal as a “desperate political move by pro-amnesty forces to provide cover to pass a bill that would otherwise not pass.”

Reports are that the senators’ package would also toughen the way businesses use the e-verify system to check the immigration status of potential employees, and that it would trim the level of Social Security benefits awarded to people who get to the end of the citizenship process.

The push for a compromise intensified Tuesday, after the Congressional Budget Office issued its double-edged analysis of the gang of eight legislation. The non-partisan analysts concluded it would reduce projected deficits by $200 billion in the next decade, because the tax revenue from economic growth would more than offset the cost in extra benefits, but would only reduce by 25 percent the flow of new people coming to the United States illegally.