When the next Congress takes office in January, with a new Republican majority in the U.S. Senate complementing an expanded Republican majority in the House, the Affordable Care Act figures to show up near the top of the agenda.

The ACA is the signature legislative achievement of Democratic President Barack Obama; it’s widely known as “Obamacare.” Republicans provided no votes in either the House or Senate to pass it, and their oft-expressed desire is to “repeal and replace” it. Notwithstanding that Obama can veto any legislation the next Congress passes — and that the Republican majorities aren’t big enough to override a veto — it’s not clear exactly how they will go about it.

They’ve come to like at least a few of its provisions, such as the one allowing parents to provide coverage under their plans to their children until the kids turn 26, and the restrictions on denying coverage due to pre-existing medical conditions. Repealing the ACA in toto and then reinstating those provisions with no lapse in coverage could be tricky.

Then there’s “Oh yeah? You got a better idea?” — a concept that goes a long way to explaining why the existing Republican majority in the House has not brought up an “Obamacare” alternative for a floor vote.

In early June, Republican U.S. Rep. Steve Scalise, of Jefferson, was pushing for a floor vote on an “Obamacare” alternative. Scalise was then chairman of the Republican Study Committee, an extra-conservative enclave within the House Republican majority, and he favored an RSC alternative to “Obamacare” that he had unveiled with some fanfare in 2013.

But the House Republican leadership, and many other Republicans, demurred. They figured the political winds were blowing in the Republicans’ favor, in part because of widespread dissatisfaction with “Obamacare,” so why mess with a good thing before the November elections? The leadership did promise Scalise that it would bring an alternative to the floor by the end of this year, an RSC aide said, even if that meant during the lame-duck session after the elections.

Scalise is no longer RSC chairman: He is now part of the Republican leadership himself, as majority whip, a post he assumed in mid-June. The elections are over, and the winds did blow the Republican way. But if the Republicans are bringing an “Obamacare” alternative to the House floor before the end of the year, they are being awfully quiet about it.

Meanwhile, Louisiana Republican U.S. Sen. David Vitter is sharpening his focus on a particular slice of the “Obamacare” pie: the so-called exemption for members of Congress and their staffs.

The issue has its roots in 2010, when the law was working its way through Congress. Republican U.S. Sen. Chuck Grassley, of Iowa, won approval of an amendment that required the federal government to stop offering members of Congress and their staffs the government-wide Federal Employee Health Benefits Plan — a typical workplace plan, with the employer paying about 75 percent of health coverage premiums and the employee paying the rest — but instead to “make available” only plans marketed through ACA insurance exchanges.

That left the members and their staffs in a sort of limbo: Unlike every other employer in the country, theirs could not offer them a standard workplace health plan and pick up most of the tab. The Obama administration then stepped in to promulgate a rule that said the government would continue to pay its share of the employees’ coverage provided they purchased it through the District of Columbia’s small-business exchange under the health law — something no other employer can do for exchange-provided coverage.

But there’s another wrinkle: The Grassley amendment allows members of Congress to designate some or all of their staffers exempt (that word again) from the amendment’s scope, pretty much at the members’ discretion.

Vitter wants to end the special treatment for Congress under “Obamacare” — by treating members and staffers in a different way that seems just as special but also somewhat punitive. Under his proposal, everyone from House Speaker John Boehner, of Ohio, to the lowliest Senate office receptionist would be required to buy health insurance through an ACA exchange — but could receive neither the employer contribution available to millions of workers across America nor the “Obamacare” subsidies available to millions more on the exchanges.

The Republican-controlled House recently rejected a similar proposal, and several Republican Senators dislike the idea, so Vitter has his work cut out for him.

Gregory Roberts is chief of The Advocate Washington bureau. Follow him on Twitter, @GregRobertsDC. For more coverage of government and politics, follow The Advocate Politics Blog at http://blogs.theadvocate.com/politicsblog/.