WASHINGTON — A bipartisan group of leading senators has reached agreement on the principles for a sweeping overhaul of the nation’s immigration laws, including a path to citizenship for the 11 million illegal immigrants already in this country.

The deal, to be announced at a news conference Monday, also covers border security, non-citizen or “guest” workers and employer verification of immigration status.

Although thorny details remain to be negotiated and success is far from certain — the legislation could run into trouble in the Republican-controlled House — the development heralds the start of what could be the most significant effort in years toward overhauling the nation’s inefficient patchwork of immigration laws.

President Barack Obama also is committed to enacting comprehensive immigration legislation and will travel to Nevada on Tuesday to lay out his vision, which is expected to overlap in important ways with the Senate effort.

The eight senators expected to endorse the new principles Monday are Democrats Charles Schumer of New York, Dick Durbin of Illinois, Robert Menendez of New Jersey and Michael Bennet of Colorado; and Republicans John McCain of Arizona, Lindsey Graham of South Carolina, Marco Rubio of Florida and Jeff Flake of Arizona.

Several of these lawmakers have worked for years on the issue. McCain collaborated with the late Democratic Sen. Edward M. Kennedy on comprehensive immigration legislation pushed by then-President George W. Bush in 2007, only to see it collapse in the Senate when it couldn’t get enough GOP support.

Now, with some Republicans chastened by the November elections which demonstrated the importance of Latino voters and their increasing commitment to Democrats, some in the GOP say this time will be different.

“What’s changed, honestly, is that there is a new, I think, appreciation on both sides of the aisle — including maybe more importantly on the Republican side of the aisle — that we have to enact a comprehensive immigration reform bill,” McCain said Sunday on ABC’s “This Week.”

“I think the time is right,” McCain said.

The group claims a notable newcomer in Rubio, a potential 2016 presidential candidate whose conservative bona fides may help smooth the way for support among conservatives wary of anything that smacks of amnesty. In an opinion piece published Sunday in the Las Vegas Review-Journal, Rubio wrote that the existing system amounts to “de facto amnesty,” and he called for “commonsense reform.”

According to documents obtained by The Associated Press, the senators will call for accomplishing four goals:

—Creating a path to citizenship for illegal immigrants already here, contingent upon securing the border and better tracking of people here on visas.

—Reforming the legal immigration system, including awarding green cards to immigrants who obtain advanced degrees in science, math, technology or engineering from an American university.

—Creating an effective employment verification system to ensure that employers do not hire illegal immigrants.

—Allowing more low-skill workers into the country and allowing employers to hire immigrants if they can demonstrate they couldn’t recruit a U.S. citizen; and establishing an agricultural worker program.

The principles being released Monday are outlined on just over four pages, leaving plenty of details left to fill in. What the senators do call for is similar to Obama’s goals and some past efforts by Democrats and Republicans, since there’s wide agreement in identifying problems with the current immigration system. The most difficult disagreement is likely to arise over how to accomplish the path to citizenship.

In order to satisfy the concerns of Rubio and other Republicans, the senators are calling for the completion of steps on border security and oversight of those here on visas before taking major steps forward on the path to citizenship.

Even then, those here illegally would have to qualify for a “probationary legal status” that would allow them to live and work here — but not qualify for federal benefits — before being able to apply for permanent residency. Once they are allowed to apply they would do so behind everyone else already in line for a green card within the current immigration system.  

That could be a highly cumbersome process, but how to make it more workable is being left to future negotiations. The senators envision a more streamlined process toward citizenship for immigrants brought here as children by their parents, and for agricultural workers.

The American Civil Liberties Union said in a statement that the framework agreed on by the senators could provide important protections for illegal immigrants who are exploited by employers and live in “constant fear” over their immigration status.

But the ACLU took issue with the proposal to require employers to use an electronic employment-verification system, calling it “a thinly disguised national ID requirement” that would undermine employees’ privacy and lead to discrimination against those “who look or sound ‘foreign.”’

Such legislation could also face long odds in the House, which is dominated by conservative Republicans and which has shown little interest in immigration reform.

The debate will play out at the start of Obama’s second term, as he aims to spend the political capital afforded him by his re-election victory on an issue that has eluded past presidents and stymied him during his first term despite his promises to the Latino community to act.

“As the president has made clear for some time, immigration reform is an important priority and he is pleased that progress is being made with bipartisan support,” a White House spokesman, Clark Stevens, said in a statement. “At the same time, he will not be satisfied until there is meaningful reform and he will continue to urge Congress to act until that is achieved.”

For Republicans, the November elections were a stark schooling on the importance of Latino voters, who voted for Obama over Republican Mitt Romney 71 percent to 27 percent, helping ensure Obama’s victory. That led some Republican leaders to conclude that supporting immigration reform with a path to citizenship has become a political imperative.