Updated at 2:28 p.m. | The White House gave a subtle nudge to a long-shot bill from two Republican senators that would overhaul the 2010 health care law as a Sept. 30 deadline to take up the measure quickly approaches.

Sens. Lindsey Graham of South Carolina and Bill Cassidy of Louisiana have been working on legislation that would incorporate much of the Senate GOP leadership-crafted health care measure that failed to pass the chamber earlier this year.

“We’ve not had any questions about Sen. Graham and Sen. Cassidy’s efforts … about progress they’re making on an effort to still keep that alive so we can complete that effort before that Sept. 30 window closes,” Marc Short, White House legislative affairs director, told reporters at the Christian Science Monitor breakfast Tuesday morning.

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Asked if the president is endorsing the Graham-Cassidy bill, Short replied: “The president continues to favor any effort to repeal and replace Obamacare. … That is a vehicle that hopefully will get more attention in coming days.”

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The Sept. 30 date is key: That is the final day Senate Republicans could move the Graham-Cassidy bill and try to pass it with 51 GOP votes under budget reconciliation rules.

Long-shot efforts

A bipartisan group of senators are eyeing long-shot legislation intended to shore up the health care law’s individual insurance market, which continues showing signs of turmoil. But Graham doubts a bipartisan bill could ever pass.

“I don’t think there’ll ever be a bipartisan fix. I don’t think that’s even possible. I have no desire to prop up Obamacare,” he said last week.

“We’re trying to find a way that’s really transformational, puts every state in the same standing,” he added.

So far, however, GOP leaders have not signaled any interest in trying to move the Graham-Cassidy bill using the reconciliation maneuver.

Sen. Rand Paul predicted there was a “zero” percent chance that the proposal gets through the Senate this month.

“I don’t really hear anybody talking about it. People are talking about it more in the media than any conversations I’m in,” the Kentucky Republican said. He was critical of the proposal because it appears to preserve taxes enacted as part of the 2010 health care overhaul.

Tax legislation

Meantime, work continues on a measure that would slash corporate and individual tax rates, while also revising the federal tax code.

To that end, Short made clear at the Monitor breakfast that the Trump administration has yet to rule out moving a tax bill under budget reconciliation rules that, like the unsuccessful health care attempt, would allow Republicans to pass a tax bill in the Senate without any Democratic votes.

Short reiterated that the president would prefer to pass a bill with support from members of both parties. But he repeatedly called doing so a “challenge,” and said his sense is many congressional Democrats are more interested in “trying to deny victory for the administration.”

“We would love to have enough bipartisan support to get 60 votes that assures permanence on tax reform,” Short said.

Thus far, however, he said administration officials have “faced resistance to that” from many Democratic members.

Trump and senior White House officials have met with 250 members from both parties to discuss a tax bill. The president will dine at the executive mansion later Tuesday evening with a bipartisan group to, in large part, discuss the matter. Short said he had talked with North Carolina Republican Mark Meadows, head of the hard-line conservative House Freedom Caucus, before arriving at the 8 a.m. Monitor breakfast.

But, notably, the longtime Capitol Hill veteran did not sound optimistic about finding the eight Democratic votes in the Senate needed to clear a 60-vote threshold on a tax measure. That would make reconciliation and a 51-vote hurdle all Republican leaders and the White House could hope to clear.

Asked when GOP leaders and White House officials would decide on a path for the tax effort, Short said a decision has to be made “sometime in October” to tee up votes on a budget reconciliation measure that would include instructions for a tax bill.

Ironing out differences

Moving a tax bill is just one of the issues the White House and GOP leaders must work out in the coming weeks and months. Another is a measure on revising the top corporate tax rate.

The president wants to lower it dramatically, from 35 percent to 15 percent. But Speaker Paul D. Ryan is openly skeptical of such an idea.

“The numbers are hard to make that work,” the Wisconsin Republicans said last week at a forum hosted by The New York Times. “Our goal is to be at or below the industrial world average, and that’s 22.5” percent, he said. “And we think that’s an achievable goal.”

The difference will have to be ironed out. So is Trump’s long-held 15 percent demand nonnegotiable?

“The president wants to get corporate rates down to 15 percent. I think it doesn’t help [Republicans] to negotiate against ourselves,” Short said. “And so, I think that we should aim for what we think is best. And I think that we all understand that there’s likely compromise to get to the best deal, but we think what’s best for the American people is a 15 percent corporate rate right now.”

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“We think that makes us more competitive on the international stage. This isn’t just about corporate rates, it’s about jobs here in our country,” he added.

Short was also asked about comments from Steve Bannon, Trump’s former chief strategist, about going to war with Ryan and Senate Minority Leader Mitch McConnell. Bannon has said the duo and other “establishment Republicans” are insufficiently loyal to the president’s agenda.

Short called Ryan and McConnell “terrific allies” on the development of the tax measure, and the push in the administration’s early months to roll back a slew of Obama-era regulations. He did not mention their efforts to repeal and replace the 2010 health care law.

“I think [Ryan and McConnell] have been strong partners in helping us enact our economic agenda,” Short said. “I think the president maintains a strong relationship with Mitch McConnell and with Speaker Ryan right now.”

He also downplayed reports that House conservatives feel left out of the party’s tax push, saying Trump and other White House officials meet regularly with Meadows and other Freedom Caucus members.

“We’re pretty well in touch with that caucus,” Short said. “I don’t sense that there’s a worry that we’re leaving them behind.”

In a lighter moment, the Washington veteran offered this observation about the Republican Party’s various factions: “I think one thing that unites members from the liberal side, the conservative side, the moderate side is they’ll all say they’re not getting enough attention — no matter what.”

Joe Williams and Niels Lesniewski contributed to this report.