Wilson Dunn, 7, who will enter the second grade this fall, is greeted by Congressman Eric Cantor (R-VA) at Two Rivers Public Charter School in Washington, D.C. on Tuesday. (Marvin Joseph/THE WASHINGTON POST)

Republican House leaders gathered at a high-performing D.C. public charter school Tuesday to promote their vision for a new federal education law to replace No Child Left Behind.

The GOP bill, known as the Student Access Act, would sharply shrink the federal role in K-12 public schools and mark a departure from the George W. Bush-era law that expanded federal authority in local school matters. The bill could go before the full House as soon as this week.

Rep. John Kline (R-Minn.) and Majority Leader Eric Cantor (R-Va.) visited the Two Rivers Public Charter School in Northeast Washington on Tuesday to tout the bill, which would give far more accountability oversight to states and promote expansion of such charter schools. Kline, chairman of the House education panel and author of the bill, was greeted by a group of fifth-graders in yellow, green and blue T-shirts dancing to Latin rhythms.

The congressmen stepped into a writing workshop for second-graders, where they asked about school assignments, birthdays and sports. Haneef Abdul-Hakim, 7, shared a story from his notebook with Cantor while Kline bent down on one knee to chat with another student. Kline said Two Rivers is a success story that shows what can be done with less federal intervention.

At a roundtable discussion with parents and school leaders, Jane Tobler, mother of two Two Rivers elementary students, explained the relief she felt when her children were selected during the school’s lottery. School officials said that only 32 spots were open this year for the elementary school’s program, and they received 1,840 applications.

“I did feel like winning the lottery,” Tobler said. “It’s so stressful, if you are not bound for any of the schools . . . you won’t know what are you going to do.”

Kline said his bill will make the lottery process easier for those trying to enroll. “We can have more parents and children winning the lottery,” he said.

The 520-page bill was passed last month by the House Committee on Education and the Workforce on a party line vote of 23 to 16. House Republicans have taken a clear turn away from Bush’s philosophy that states receiving billions of dollars each year in federal aid should be accountable to Washington.

In the Senate, Democrats passed their own education bill in the Committee on Health, Education, Labor and Pensions that would maintain much of the federal education oversight.

The question is whether House Republicans and Senate Democrats can find consensus and pass a single bill, something many observers say seems unlikely in the current Congress. Cantor said Republicans have been working diligently to find compromise.

“We intend to bring support from both sides,” Cantor said.

No Child Left Behind sets conditions and requirements for every public school receiving federal funds to educate poor students and those with special needs. The law defines academic progress and stipulates sanctions for schools that don’t meet that progress. It also dictates specific improvement strategies that the states must adopt for their weakest schools. It passed Congress in 2001 with bipartisan support; key sponsors included now-House Speaker John A. Boehner (R-Ohio), and Sen. Edward M. Kennedy (D-Mass.), who died in 2009.

There is evidence that shows U.S. students have steadily improved in math and reading since 2004, when No Child Left Behind began taking effect, and that the achievement gap between racial groups has narrowed.

The proposed legislation would retain the No Child Left Behind requirements that schools test students annually in math and reading from grades 3 through 8 and once in high school. But states would be able to set their own academic standards, decide whether schools are meeting them and determine what to do about underperforming schools. The plan gives districts more freedom in spending federal funds.

It also would promote the expansion of charter schools, an element that drew some support from Democrats when it was introduced as a stand-alone bill in the last Congress two years ago. That bill never became law.

Kline has said his proposal would “cut through the dizzying maze of mandates, reporting requirements and strict funding rules that make it difficult, if not impossible, for states and districts to improve performance and narrow achievement gaps.”

Kline’s bill also would freeze education spending at sequester rates instead of restoring federal dollars to pre-sequester levels.

Cantor has offered an amendment that calls for Title 1 funds, which schools use to help educate poor students, to follow students if they transfer to other public schools, including charter schools. The money currently flows to schools with high poverty rates, not to individual students.

Opponents say Kline’s bill would weaken the accountability of schools serving low-income, minority and special-education students.

Democrats and Republicans agree on one thing: They want to erase the most unpopular aspect of No Child Left Behind, the requirement that students become proficient in math and reading by 2014, or their schools face escalating penalties.