This week: West Wing turnover, trade war, gas prices and more

Here are the stories our D.C. insiders are talking about in this week's "Inside Politics" forecast, where you get a glimpse of tomorrow's headlines today.

1. West Wing turnover coming?

The start of summer could coincide with the beginning of more West Wing turnover.

Last July saw the departures of Reince Priebus and Sean Spicer. This year White House observers are watching for whether their successors John Kelly and Sarah Sanders follow their lead. Michael Shear of The New York Times said Kelly has been "essentially invisible as chief of staff for weeks now."

"There's rumors almost every day that his departure is coming," Shear said. "And keep your eye ultimately on when Sarah Sanders leaves, because while she says she's not going anywhere, she's been in the job for close to a year now. If she leaves, you're likely to see an entire turnover of her press staff."

2. Trump aide legal fund details

The end of the second quarter means it's time for political action committees to disclose their fundraising numbers from the past three months. Weekly Standard senior writer Michael Warren says he's particularly interested in the Patriot Legal Expense Fund Trust -- the PAC set up to help associates of President Trump pay legal bills incurred from the Russia investigation.

"It's a pretty unusual organization," Warren said. "Some Democrats are raising questions about the connection that this PAC will have with the Trump re-election campaign. I'm just looking to find out who donated to this and who's getting the money. We haven't found any of those answers yet."

3. Filibuster fight

Trump has called again and again for the Senate to eliminate the filibuster -- which would allow the GOP to pass almost anything it wants without a single Democratic vote. And now a senior Senate Republican says he may agree, reports Politico's Rachael Bade.

"There was a meeting at the White House this week where the president and House Republicans tried to make the case to a bunch of [Senate] Republicans," Bade said. "Basically they argued that 'you did this for the Supreme Court and look what happened? We have a great justice. You should do the same thing for appropriations.'"

And they may have won over the senior senator from Alabama -- Richard Shelby, who chairs the Appropriations Committee.

"He apparently told the President, 'Okay, I can back this even though Mitch McConnell is opposed to it.' And I think we're going to see a big assault on the filibuster in the coming months," Bade said.

4. GOP lawmakers struggle with Trump trade policy

Trump's trade war continues to escalate, with new retaliatory Canadian tariffs on US goods coming into effect on Sunday. And that's causing a lot of heartburn among Senate Republicans.

"You saw Senate Republicans becoming more and more aggressive this past week against the President and his trade policies," Washington Post reporter Seung Min Kim said. Sens. Bob Corker and Pat Toomey are pushing a bill that would give Congress more oversight over the President's trade policy authority.

For now, Senate Majority Leader Mitch McConnell is blocking their bill from coming up for a vote. "But if that vote happens, it's going to be one that really puts a lot of Republicans in a tough spot: either endorse their core ideology of free trade, or go along with the President of their party who's an incredibly popular figure with their voters," Kim said. "This is going to be a battle that continues to heat up."

5. Pain at the pump

And from CNN Chief National Correspondent John King:

The President is ignoring Republican complaints that his trade war could end up hurting the GOP in the midterms. But he is trying to respond to another economic worry -- even though he twisted the facts in a tweet about it.

Gas prices are up 60 cents a gallon over the past year -- and Republicans worry that takes a summer bite out of their big tax cut. The President tweeted Saturday that the King of Saudi Arabia promised to help by producing more oil. But the White House had to correct the record later -- to say King Salman did not promise anything other than to maintain the standard level of Saudi reserves, and to keep in touch with OPEC partners about the market.

By John King & Ben Geldon. The-CNN-Wire™ & © 2018 Cable News Network, Inc., a Time Warner Company. All rights reserved.

The Gayly – July 1, 2018 @ 11:45 a.m. CDT.