Last month, nearly immediately after he announced that he could not support the first version of the Senate's healthcare bill, a Trump-aligned super PAC - America First Policies - announced an ad campaign slamming Mr Heller for the decision.
Senate Republican leader Mitch McConnell thus has scheduled a vote early next week to repeal Obamacare.
At that lunch, beneath the portrait of Abraham Lincoln in the White House's State Dining Room, Trump made clear he wanted the senators to go back to the drawing board before heading out on vacation in August.
US President Donald Trump has called on Senate Republicans to postpone their summer holiday until they have kept their promise to ditch Obamcare. "And this bill is on my desk and we can sign it and celebrate for the American people".
Conservative Rand Paul of Kentucky said he would only support a repeal-only bill.
McConnell said he expects senators to vote next week to consider the new health care bill. They can keep talking among themselves in an attempt to come up with another Republican-only plan.
One Republican senator who didn't attend the luncheon was Senate intelligence committee Chairman Richard Burr.
The bill the House of Representatives passed in May by a narrow margin had attracted 40 per cent support.
Conceding they were wrong may sting, but the reality is that most Americans like the key provisions of Obamacare, and it has so far achieved one of its most important goals: slowing the growth of health care costs.
"It's time for Congress to pivot away from the bills that are going nowhere", said House Minority Leader Nancy Pelosi.
It's why the various Senate tweaks to the Better Care Reconciliation Act-repealing fewer of Obamacare's tax hikes, say, or throwing $45 billion at opioid addiction-have no impact on the CBO's coverage estimates.
"We still do have work to do to get to a vote of 50, but people are committed to continuing that work", said Sen.
Trump seemed to push this approach Tuesday. "It really means, can we come together as a conference, can we come together as a Republican Party, can we come together on a signature piece of legislation we've talked about for seven years".
Democrats, who are united in their opposition to the Republican efforts and reveled in this week's deadlock, told Republicans to abandon their healthcare efforts as they appeared no closer to reconciling policy differences after Wednesday's meeting.
White House aides said they hope an agreement can be worked out by next week. But Republicans' slim majority in the Senate isn't going to get any bigger before the 2018 midterm elections, and it could get smaller after that.
It takes just two Republicans to block the bill. Eliminating the deduction would raise about $1.3 trillion over the next decade, which could pay for a lot of other tax cuts.
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