WASHINGTON (AP) — Republicans are “in a demographic death spiral” and will fail in their effort to win the presidency if the party blocks an immigration overhaul, a leading GOP senator said Sunday.

Sen. Lindsey Graham, the South Carolina Republican who helped write a bipartisan immigration bill under debate in the Senate, said conservatives who are trying to block the measure will doom the party and all but guarantee a Democrat will remain in the White House after 2016’s election.

A Democrat also involved in developing the proposal, Sen. Robert Menendez of New Jersey, went a step further and predicted “there’ll never be a road to the White House for the Republican Party” if immigration overhaul fails to pass.

Meanwhile, one the proposal’s authors who is considering such a White House campaign refused again to pledge support for the measure without changes conservatives have demanded.

“The vast majority of Americans, the vast majority of conservative Republicans are prepared to support immigration reform, but only if we can ensure that we’re not going to have another wave of illegal immigration in the future,” said Sen. Marco Rubio, R-Fla.

The Senate last week overcame a procedural hurdle in moving forward on the first immigration overhaul in a generation. Lawmakers from both parties’ voted to begin formal debate on a proposal that would give an estimated 11 million immigrants in the U.S. illegally a long and difficult path to citizenship.

The legislation also creates a low-skilled guest-worker program, expands the number of visas available for high-tech workers and de-emphasizes family ties in the system for legal immigration that has been in place for decades. It also sets border security goals that the government must meet before immigrants living in the U.S. illegally are granted any change in status.

“I think 95, 96 percent of the bill is in perfect shape and ready to go. But there are elements that need to be improved,” said Rubio, refusing to say if he’ll vote for the measure he helped write unless changes are made.

Republicans are demanding tougher border security measures and stricter standards for who qualifies for government programs such as Social Security and health care.

Rubio is trying to balance concerns from his party’s conservative flank that has great sway in picking a nominee with the political attempt to win over Hispanic and Asian American voters who overwhelmingly favored President Barack Obama’s re-election in 2012. Further complicating Rubio’s presidential aspirations, the Republican-led House is considering its own version of immigration proposals that more closely follow their own perspective, which hews toward tea partyers.

“After eight years of President Obama’s economic policies, and quite frankly foreign policy, people are going to be looking around,” Graham said. “But if we don’t pass immigration reform, if we don’t get it off the table in a reasonable, practical way, it doesn’t matter who you run in 2016. We’re in a demographic death spiral as a party and the only way we can get back in good graces with the Hispanic community in my view is pass comprehensive immigration reform. If you don’t do that, it really doesn’t matter who we run in my view.”

In 2012, Obama won re-election with the backing of 71 percent of Hispanic voters and 73 percent of Asian voters. A thwarted immigration overhaul could send those voting blocs more solidly to Democrats’ side in future elections. That has led some Republican lawmakers to support immigration reform, but the party’s conservative base still opposes any legislation that would create a pathway to citizenship for immigrants living here illegally.

Democrats are well aware of the numbers.

“I would tell my Republican colleagues, both in the House and the Senate, that the road to the White House comes through a road with a pathway to legalization,” Menendez said. “Without it, there’ll never be a road to the White House for the Republican Party.”

Graham spoke on NBC’s “Meet the Press.” Menendez was interviewed on CNN’s “State of the Union.” Rubio was on ABC’s “This Week.”

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