Story highlights House Speaker John Boehner enrolled online in the D.C. Obamacare exchange last week

The experience was "pretty frustrating," the top House Republican said

Boehner's premiums under Obamacare will nearly double from his current plan

But he gets some help from the government in covering his new costs

The top Republican leading the charge against Obamacare is now signed up for it and will take thousands of dollars in government support to help with its costs, a spokesman for House Speaker John Boehner confirmed to CNN.

Boehner's premiums for his new plan under the Affordable Care Act will nearly double from his current monthly payments, even with the federal contribution.

All of this was set in motion last week when the Speaker enrolled for coverage on the D.C. exchange established under the health reforms championed by President Barack Obama but opposed by Republicans on Capitol Hill.

Boehner said the experience was "pretty frustrating" and his office sent pictures of him trying to log onto the website, the rocky rollout of which has been a rallying point for renewed Republican criticism of the law as unworkable.

Once he got through the system, Boehner's office said he chose an individual plan that was similar to the Blue Cross Blue Shield one he has now as part of the federal employees health package.

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If members of Congress want health coverage facilitated by the government acting as their employer, they now must sign up with Obamacare.

Boehner saw an eye-popping jump in cost as he moved from a plan set up for millions of federal workers to the D.C. exchange, which is designed for small businesses and individuals.

The current cost for Boehner and his wife? They "pay a monthly premium of $433," said Boehner spokesman Brendan Buck.

The new plan for the two of them?

It "would cost $802 per month in premiums," Buck said.

That is an 85% leap. But, Boehner's wife is about to go on Medicare, so he will get an individual plan. That cost? $449 a month.

Boehner's office notes he will now be paying more for one person in the Obamacare exchange than he was for two people in the federal employees plan. Deductibles for the Boehners will jump from $700 to about $2,000.

Why did Boehner's premium go up so much? One reason, his age.

Under the Affordable Care Act, health insurers can no longer set different prices based on health. The law instead gives just a few variables they can consider. At the top of that list is age.

Many congressional staffers were shocked to see how much more a 60-year-old staffer would pay for the same plan than a 26-year-old colleague.

"The monthly formula for older workers is a serious, serious hit," one congressional employee said at the time. "In addition to what I'm paying now, it will be another $300 to $400 a month."

Boehner, who turned 64 last week, is at the upper end of the age spectrum for Obamacare. At 65, members can sign up for Medicare.

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Many may point out that he is also a smoker, a condition for which insurers could charge more under the law. But, Boehner may be in luck. The D.C. exchange has ruled smoking should be considered a pre-existing condition and insurers in that market cannot increase premiums because of it.

But the biggest help for the Speaker is a contribution offered to federal workers on the D.C. exchange to help with premiums. Private employers pick up some of the cost for their employees as well.

Boehner's office confirms he will accept the contribution, despite his public push against such assistance for plans covering members of Congress. He will receive $5,113 in federal premium support over the next year.

When asked why his boss is accepting the contribution now, Boehner spokesman Michael Steel told CNN that "Washington Democrats chose not to make that change."

CNN pointed out that several other members of Congress chose to return their premium support to the Treasury. Boehner's office did not respond further when asked whether he considered that option.