Washington (CNN) Raising the retirement age, implementing means-testing and encouraging more retirement plans for workers are among the solutions that Jeb Bush is proposing Tuesday to help stabilize and preserve Social Security and Medicare for seniors.

"If we do not have an honest conversation about what it will take to protect Medicare and Social Security, we fail seniors and we will fail the next generation of Americans," Bush says in a Medium post set to publish on Tuesday.

The Republican presidential candidate, according to information provided by his campaign, favors raising the retirement age for Social Security beyond its current target age of 67, starting in 2022 by gradually increasing the age by one month every year. That means by 2058, when life expectancy is expected to be longer, workers would have to be 70 to claim full benefits -- or 65 for early benefits.

The campaign stressed that under Bush's plan, current retirees or those near retirement won't see a cut to their benefits.

For those who want to stop working before the retirement age, Bush would favor decreasing the size of their Social Security checks even more than the current reduction for retiring early, while increasing checks for seniors that choose to work beyond the age threshold.

He would do that by eliminating a provision that gives less Social Security to those who work and make more than $15,720 a year during retirement, meaning seniors would get their full Social Security benefit check on top of whatever they make in their post-retirement job.

He would also get rid of a 6.2% payroll tax on seniors who work beyond the retirement age.

But the wealthiest of workers, under his plan, would get smaller Social Security checks during retirement and fewer subsidies for Medicare, otherwise known as means-testing.

While his brother, former President George W. Bush, pursued a controversial plan to privatize Social Security, Jeb Bush said in August that he doesn't plan to take a similar path.

"It would have made sense back then, now we're way beyond that," Bush said at the Iowa State Fair. "What we need to do is reform Social Security to preserve it and protect it for those that already have it and reform it in the logical ways where there's broad bipartisan consensus, which is to, over an extended period of time, raise the retirement age and raise the income cap limit. You can solve Social Security that way."

For Medicare, Bush praised the structure proposed by Rep. Paul Ryan that would move toward privatization. He said he would allow seniors to keep their Health Savings Accounts, and he would push for new plan options.

"Seniors will still get a simple brochure in the mail from the government every fall," Bush says in the post. "They will be able to review and choose from their local options from Humana, Anthem, United or another private plan, or traditional Medicare. Seniors will have access to new options, like plans that specialize in treating congestive heart failure or diabetes or Alzheimer's."

Photos: Jeb Bush's life Photos: Jeb Bush's life Former Florida Gov. Jeb Bush waves as he takes the stage as he formally announces he is joining the race for president with a speech June 15, 2015, at Miami Dade College in Miami. Hide Caption 1 of 21 Photos: Jeb Bush's life Former Florida governor Jeb Bush shakes hands with attendees after speaking at the 42nd annual Conservative Political Action Conference on February 27 in National Harbor, Maryland. Hide Caption 2 of 21 Photos: Jeb Bush's life Bush takes a selfie with a guest at a luncheon hosted by the Chicago Council on Global Affairs on February 18 in Chicago. Bush delivered his first major foreign policy speech at the event. Hide Caption 3 of 21 Photos: Jeb Bush's life Bush hands out items for Holiday Food Baskets to those in need outside the Little Havana offices of CAMACOL, the Latin American Chamber of Commerce on December 17 in Miami. Hide Caption 4 of 21 Photos: Jeb Bush's life Bush waves to the audience at the Tampa Bay Times Forum in Tampa, Florida, on August 30, 2012, on the final day of the Republican National Convention. Hide Caption 5 of 21 Photos: Jeb Bush's life Bush (left) and wife Columba Bush attend the 2012 Lincoln Center Institute Gala at Frederick P. Rose Hall, Jazz at Lincoln Center on March 7, 2012, in New York City. Hide Caption 6 of 21 Photos: Jeb Bush's life President Barack Obama (left) speaks about Bush (center) while visiting Miami Central Senior High School on March 4, 2011 in Miami, Florida. The visit focused on education. Hide Caption 7 of 21 Photos: Jeb Bush's life Bush (left) speaks with Brazilian President in charge Jose Alancar during a meeting at Planalto Palace in Brasilia, April 17, 2007. Bush was in Brazil to speak about sugar and ethanol business. Hide Caption 8 of 21 Photos: Jeb Bush's life Then-Texas Governor Rick Perry (center) testifies as Bush (right) and then-Arizona Governor Janet Napolitano (left) listen during a hearing before the House Committee on Homeland Security on Capitol Hill October 19, 2005. Hide Caption 9 of 21 Photos: Jeb Bush's life Bush gives a thumbs up signal from his car as he leaves a local polling station after casting his vote in Coral Gables, Florida, November 5, 2002. Hide Caption 10 of 21 Photos: Jeb Bush's life Bush walks out of the West Wing after meeting with his brother, then-President George W. Bush, at the White House January 9, 2002. Governor Bush participated in the signing ceremony of the Everglades Protection Agreement. Hide Caption 11 of 21 Photos: Jeb Bush's life Then-Mexican President Vincente Fox (left) and Bush hold a press conference September 7, 2001, in Miami. Fox visited Florida to attend the Americas Conference and deliver a speech to speak about issues such as immigration. Hide Caption 12 of 21 Photos: Jeb Bush's life Then-President George W. Bush (right) is greeted by Jeb Bush on March 21, 2001, at Orlando International Airport in Orlando, Florida. President Bush was in Orlando to attend the American College of Cardiology Annual Convention. Hide Caption 13 of 21 Photos: Jeb Bush's life Bush speaks during a press conference at the Carandolet Government Palace in Quito, January 18, 2006. Bush and a businessmen delegation were in a two-day visit to talk about a free trade agreement. Hide Caption 14 of 21 Photos: Jeb Bush's life Bush speaks to reporters after meeting with the Florida State Cabinet at the Florida State Capitol Building November 16, 2000, in Tallahassee, Florida. Hide Caption 15 of 21 Photos: Jeb Bush's life Then-President George W. Bush (left) and Jeb Bush (right), raise their arms onstage following a rally at the Florida State Fairgrounds, October 25, 2000, in Brandon, Florida. Hide Caption 16 of 21 Photos: Jeb Bush's life Jeb Bush (left) and then-President George W. Bush stand with their arms around each other's shoulders at a rally in Miami, Florida, September 22, 2000. Hide Caption 17 of 21 Photos: Jeb Bush's life Then-President George W. Bush (right) and Jeb Bush go through the line for strawberries during a stop at the Stawberry Festival March 12, 2000 in Plant City, Florida. Hide Caption 18 of 21 Photos: Jeb Bush's life The Bush family, (left to right) former U.S. President George W., former Florida Governor Jeb, former President George H.W. and his wife Barbara, watch play during the Foursomes matches September 25, 1999 at The Country Club in Brookline, Massachusetts the site of the 33rd Ryder Cup Matches. Hide Caption 19 of 21 Photos: Jeb Bush's life Former President George H.W. Bush (second left), his wife Barbara Bush (left), their son Jeb Bush (center), then-first lady Hillary Clinton (second right), and former then-President Bill Clinton (right) look up to see the U.S. Army Golden Knights parachute team November 6, 1997 at the conclusion of the dedication ceremony of the George Bush Library in College Station, Texas. Hide Caption 20 of 21 Photos: Jeb Bush's life Portrait of the Bush family in front of their Kennebunkport, Maine house August 24, 1986. Pictured, back row: Margaret holding daughter Marshall, Marvin Bush, Bill LeBlond. Pictured, front row: Neil Bush holding son Pierce, Sharon, George W. Bush holding daughter Barbara, Laura Bush holding daughter Jenna, Barbara Bush, George Bush, Sam LeBlond, Doro Bush Lebond, George P. (Jeb's son), Jeb Bush holding son Jebby, Columba Bush and Noelle Bush. Hide Caption 21 of 21

Earlier this year, Bush took heat from critics after saying in New Hampshire that he wants "to phase out this program for others and move to a new system that allows them to have something."

After Democrats pounced, accusing the candidate of wanting to destroy entitlements , Bush pushed back , saying he wanted to "reform" the program, not eliminate it.

To help increase retirement savings plans, Bush would encourage "starter 401(k) plans" for small business employees whose employers can't afford to contribute to plans. He also favors the idea of letting small businesses pool together to access a retirement savings plan for their employees.

As for those who already divert a portion of their paycheck to a private savings account, Bush would get rid of the 10% limit that's allowed.

Maya MacGuineas, head of the Campaign to Fix the Debt, praised Bush for a laying out a "thoughtful and serious plan."

"At the same time, it is both unfortunate and disappointing that he has also proposed large tax cuts that would cost more than these entitlement reforms will save," MacGuineas said in a statement. "Still, today's plan represents a tremendously important starting point for a real debate on the future of Social Security and Medicare."

The presidential campaign for Gov. Chris Christie argued Tuesday that the New Jersey governor has long been out front on this issue, pointing to the entitlement policy he laid out in April. Just hours before Bush released his proposal, Christie's campaign put up a video, "The Only One With A Plan."

It's not the first time Christie has tried to draw a contrast with Bush on entitlements. Shortly after Bush fell under scrutiny for his comments about "phasing" out Medicare, Christie went on the attack.