By John King, CNN Chief National Correspondent

(CNN) -- President Trump faces huge personnel and policy decisions while visiting the Hill this week to push tax reform. His upcoming trip to Asia could be ... complicated. And will he push for a new Fed Chair to replace Janet Yellen?

These stories and more are part of this week's "Inside Politics" forecast, where the best reporters in Washington give you a taste of tomorrow's headlines today.

1) Trump goes to Capitol Hill

President Trump makes a rare foray to Capitol Hill on Tuesday to meet with Senate Republicans over lunch. Their shared goal of tax reform is the top agenda item, but the visit will put the president in the same room with a good number of GOP lawmakers who view him warily or don't trust him outright.

Among the invited guests: Sen. Bob Corker of Tennessee, who recently cracked a joke -- well it was sort of a joke -- about a presidential competency test. Plus Sen. John McCain, who has sparred with the President on a number of issues. And Sen. Jeff Flake, Arizona's other Republican senator, who Trump has promised to help defeat in a primary next year.

Fun, right?

CNN's Jeff Zeleny reports that the White House wants the attention to be on tax reform, but Trump's unpredictability and a tense environment could make for a hold-your-breath moment:

"So many senators have questions for him. [Senator] John McCain has been really a rising voice, as we've heard, " Zeleny explains. "My question is, what are the questions these senators have for the president, and how will this one-on-one interaction on Capitol Hill work for him? Because he needs them, but he often wants to distance himself from them."

2) New White House take on health care reform?

While on the Hill, maybe President Trump will offer some clarity about whether he wants another try at passing a big health care bill in 2017.

He made people rather dizzy last week by taking several positions on a bipartisan measure put forward by Sens. Lamar Alexander and Patty Murray.

Now, CNN's Phil Mattingly reports the White House has sent a list of proposed changes to the so-called Alexander-Murray bill to test whether it is possible to expand the measure and perhaps gain it some conservative support.

"Some of the principles, whether it be relief from the individual and employer mandate, retroactive on the employer side, expansion of short-term health savings accounts, and more regulatory relief, probably would be non-starters for Democrats on their face," Mattingly reports. "It shows an actual legitimate engagement from the legislative affairs team from the White House, showing that, 'Look, we might actually be willing to get on board on this.'"

3) Trump's thorny Asia trip

President Trump has a packed calendar for an upcoming Asia trip that includes stops in South Korea, Japan, China, Vietnam and the Philippines.

These long, grueling trips are worked out well in advance, but with just 10 days until the President hits the road, some decisions are still in flux.

Julie Hirschfeld Davis of The New York Times notes that Trump is not thrilled about the prospect of spending time with President Duterte of the Philippines. And there is a debate within the administration about whether the President should visit the Demilitarized Zone that separates North Korea and South Korea.

"There's a lot of worry that the President, who we know is prone to some inflammatory statements, might say or do something inappropriate there," Davis says. "And, of course, you know, this whole situation is on a hair trigger with North Korea, to coin a phrase. There's also some debate about whether he should go to the Philippines. He actually alluded to that last week -- he said he might not really want to go (but) ... he's accepted an invitation to attend a summit there."

4) Does Trump want a new Fed Chair?

Most administration insiders believe President Trump will pick one of two conservatives to be the next chair of the Federal Reserve.

But current Fed Chair Janet Yellen is not without deep support, even among some Republicans.

These backers understand that keeping Yellen may be a tough sell. The Fed pick is a plum job and the President values the chance to bring loyalists into the administration.

So Kimberly Atkins of the Boston Herald reports those pushing for Yellen to get another term are reading the President's Twitter feed and trying to play to his love of anything that can be cast as a win.

"People backing [Yellen] are ... playing to the president's love for bragging. Recently he has bragged a lot about how strong the stock markets are. We see him tweet about that frequently," she says. Yellen backers may argue to Trump that "a change at the top of the Fed could have a negative impact on markets, and you wouldn't be able to brag about that anymore," she says. "So we still don't know what he's going to do."

5) Make no mistake: 43's speech was aimed at 45

Aides to former President George W. Bush insist his big speech last week in New York was no big deal and that the themes and and issues he covered were all staples of his presidency.

That's true when it comes to such issues as immigration, trade, globalization or the former President's worries that nationalism can too easily morph into nativism.

But Bush was not just repeating his greatest hits. The speech appeared to have been organized, top to bottom, to challenge President Trump on both substance and tone.

The effort by aides to play it down is consistent with 43's long-held view that former Presidents should whenever possible steer clear of current debates. Bush reportedly has no interest in a daily back and forth with Trump.

But friends and associates say that President Bush understood the implications of the moment and knew his speech would get attention.

It was born, these friends say, of a frustration shared by both Presidents Bush that not enough senior voices in the GOP are challenging an administration they view as bad for the Republican Party and for the country.