Senate Homeland Security and Governmental Affairs Committee Chairman Ron Johnson speaks on Capitol Hill in 2016. Shawn Thew / EPA file

"Its something the president should do," Robert Moffit, a senior fellow at the Heritage Foundation who has tracked the issue, told NBC News. "Beyond the separation of powers question...they shouldnt be getting special advantages at the expense of the taxpayer."

Since members make too much money to qualify for Obamacare subsidies, theyd have to pay the full cost of the premiums, which would be a major increase.

Congress could pass legislation to grant themselves their current benefits, but theyd face taunts from Trump and other critics accusing them of voting to enrich themselves. Theres a reason they havent resolved the issue up to this point.

But its possible the move could come off as unnecessarily cruel. After all, it wouldnt just be elected officials with six-figure incomes who would be affected.

"While people are maybe not sympathetic to members of Congress, more would be sympathetic to the staff and it would be a far, far bigger deal for the staff," Len Nichols, Director of the Center for Health Policy Research and Ethics at George Mason University, told NBC news.

It could also backfire if Congressional Republicans resent the move and become less cooperative. Senators, in particular, have proven increasingly willing to buck the president and he cant afford to lose more support and follow through on his agenda.

Trump has said Congress should not vote on any other legislation until lawmakers pass health care.

This one is harder to pull off. The legislative branch sets its own rules, follows its own schedule, and its members can get prickly if they believe the executive branch is muscling in on its territory.

"He and his team have to understand that Congress is a co-equal branch of government," said Jim Manley, a former top aide to Senator Harry Reid. "They dont respond well to threats from any president of either party."

Trump couldn't stop Congress from voting on legislation. If he really wanted to, though, he could veto all bills until members caved.

He would be picking an especially dangerous time to issue a blanket veto threat. Over the next few weeks, Congress needs to pass legislation to fund the government or there will be a shutdown. It also needs to raise the debt limit or it risks setting off a financial crisis. Neither scenario would be a good look for the party with unified control of government.

Trump also cant keep up a blockade indefinitely without threatening the next item on his agenda: Taxes. The House and Senate are using this years budget reconciliation process to try and pass health care. But the fiscal year ends September 30, and once Congress passes a new budget, the legislation will expire. The new reconciliation bill is supposed to be the vehicle for tax reform, which promises to be a difficult fight as well.

For their part, members of Congress dont sound too intimidated so far.

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Health Care: President Trump's Triple Threat - NBCNews.com