The rotunda is seen June 21, 2012, at the University of Virginia in Charlottesville. (Norm Shafer/For the Washington Post)

The rejection letter Amanda Scarangella received last year from the University of Virginia set off a tear-soaked night for the Ashburn teen.

For Scarangella, who took seven Advanced Placement courses at Stone Bridge High School and participated in an elite girls leadership training program, the rejection letter was a shock. For her parents, who moved to Northern Virginia because of its strong public schools and access to renowned public colleges, it was frustrating.

“We felt like when you have a 4.28 grade-point average and great board scores, you should have a good chance of getting into the state University of Virginia,” said her father, Dave Scarangella.

As another round of high-performing seniors in Washington’s high-performing suburban schools put the finishing touches on their college applications, there is a new wave of angst over whether there will be space for them in Virginia’s premier schools.

For years, some Northern Virginia lawmakers have proposed expanding access to state schools by tightening limits on the number of out-of-state students schools can accept. This year, some local elected officials are taking up the fight as well.

The Loudoun County Board of Supervisors approved a legislative agenda this fall that proposes a 25 percent cap on the portion of out-of-state students in Virginia’s institutes of higher education. They started lobbying state lawmakers this week.

Past efforts have failed, pitted against the enduring financial struggles of the state’s colleges and universities. Out-of-state students have long been sought-after by universities seeking to create diverse communities and to recruit the most talented students. But in recent years, as state per-pupil spending has dwindled, out-of-state students are especially treasured for the higher tuition they pay. In Virginia, some universities charge more than twice as much for out-of-state residents.

But Supervisor Ken Reid (R-Leesburg) called it a pressing “bread-and-butter issue” for Virginia’s families. As the father of two high school-age children, he knows the nervous calculations families make.

“Am I going to have to pay $60,000 at a private school, versus $25,000 to $30,000 each year at a public school?” Reid asked. “It’s a major, major concern.”

While Virginia lawmakers weigh efforts to limit out-of-state enrollments, some states have raised their caps in recent years. Arizona increased its nonresident cap from 30 percent to 40 percent, and Wisconsin bumped up its cap from 25 percent to 27.5 percent.

Virginia law says universities that have exceeded 25 percent nonresident enrollment should not increase their share of out-of-state students further. Four schools have surpassed that threshold: the College of William and Mary, the University of Virginia, Virginia Tech and James Madison University.

William and Mary has the highest rate of out-of-state students, between 36 percent and 38 percent in recent years, according to the State Council of Higher Education for Virginia. U-Va. has hovered around 33 percent.

Universities typically oppose a strict cap, citing the possible financial ramifications. Many lawmakers fear the loss of out-of-state tuition revenue could lead to controversial spikes in tuition for in-state students.

An analysis of a bill sponsored by Del. Timothy Hugo (R-Fairfax) last year showed that enforcing a 25 percent cap would add nearly 7,000 spots for in-state students at the state’s public colleges, but it also would cost $51 million in extra revenue from the general fund and cause the universities to lose $150 million in tuition revenue.

Most Virginia lawmakers favor expanding access by increasing the size of the university system.

The Virginia Higher Education Opportunity Act of 2011, a chief accomplishment of Gov. Robert F. McDonnell (R), provided new funding — after years of declines — to help universities grow to meet the goal of awarding 100,000 more college degrees by 2025. The schools are increasing their in-state and out-of-state slots.

U-Va. has increased its offers of admission to Virginia students by 10 percent, growing from 3,429 in 2009 to 3,733 in 2013. Out-of-state admissions offers have increased proportionally, school spokesman McGregor McCance said.

About 168,200 undergraduates are enrolled this fall in Virginia’s public four-year universities, up from 166,700 a year ago. Demand is highest for admission to the two most prestigious: U-Va. and William and Mary. Nationally, however, experts say there are signs of weakening demand for colleges that are not in the top tier.

The appetite for seats in Virginia’s top universities is voracious among aspiring students in Northern Virginia’s growing suburbs. Hugo said he plans to introduce another bill in the 2014 session to cap out-of-state enrollment because he sees such a large number of students with outstanding academic records getting turned away.

“With U-Va. and William and Mary, they see their peer group as Harvard and MIT, but they forget they are public institutions and they have a responsibility to the students of Virginia and the families of Virginia,” he said.

Many parents were alarmed by a U-Va. working group’s report made public this fall that said the school should sever some ties to the state in order to firm up its finances, pursue more out-of-state students and become more globally competitive.

McCance said the university did not adopt the proposal as part of its strategic plan and is “thoroughly committed to its role as a public university that serves the Commonwealth, nation and world.”

Kirsten Nelson, director of communications and government relations for the State Council of Higher Education for Virginia, acknowledged that Northern Virginia families are in a bind. But she encouraged them to look beyond their first-choice schools.

“If your child wants to go to college in Virginia, they will find a good match,” she said. “It may not be perfect, but they can find a good match.”

After Amanda Scarangella, 18, of Loudoun County, was turned down by U-Va. last year, she said she was “very disappointed for a very long time.” But she was ultimately accepted to Virginia Tech, her father’s alma mater, where her family is paying in-state tuition.

Now, as a freshman there, she said she feels “exhilarated” by her new school. She loves meeting friends from different places and is planning to major in psychology. “It’s really become a home to me,” she said.

Nick Anderson contributed to this report.