A new wave of political pressure greeted Federal Reserve Chair Jerome Powell and his colleagues as they gathered in Washington this week to discuss the direction of interest rates.

From the right, GOP presidential candidate Donald Trump again raised the prospect of putting Powell out of a job. "I know a lot about firing people," the former President teased in an interview with a TV station in Arizona.

From the left, the commentary came in the form of two new letters from liberal lawmakers calling on Powell to immediately lower interest rates. One letter, led by Sen. Elizabeth Warren, concluded by telling the central banker "you have kept interest rates too high for too long."

But the political noise may have a limited impact, for this week at least. It's partly because of the limited leverage these politicians hold at the moment but also in large part by Powell's own design.

The central banker has long set "data driven" benchmarks (and tried to hew closely to them) to avoid the fate of predecessors seen as too susceptible to changing political winds.

Powell maintains that his sole focus is on things like a strong jobs report last week as well as another inflation print due Wednesday morning.

Desmond Lachman describes it as a strategy of essentially backing oneself into a corner — intentionally.

"Given the way he's set this thing up, the bar is going to be very high for him now to cut interest rates before the election," said Lachman, a former managing director at Salomon Smith Barney currently at the American Enterprise Institute.

"That's really the box that he's put himself into," Lachman added.

There's also little these critics can do at the moment. Trump has been clear that if he wins Powell will be out a job no matter what he does, but the question is whether Trump would take the destabilizing step of firing him or simply letting his term expire.

Mark Spindel, the chief investment officer of Potomac River Capital and a Fed historian, notes that both President Joe Biden and Powell would welcome the declaration of an economic soft landing but Powell is fully committed to waiting for a consensus on the data.

"I don't think Jay has wavered in what he wants to do but I don't think he wanted to get almost ahead of himself," Spindel said, adding "certainly the window to offer policy accommodation before the election...is closing fast."

Trump's ongoing pressure campaign

The Fed is widely expected to keep its rates at a 23-year high Wednesday, meaning no near-term relief from elevated borrowing costs.

Those high costs — especially for getting a mortgage — is why many in the political world are pushing for quicker action from the Fed to lower rates.

Housing is why Trump's questioner last week — ABC15 Arizona's Rachel Louise — brought up monetary policy during his stop in Phoenix. Trump focused on interest rates and energy prices, saying "with me, they're coming down, interest rates are coming down, energy is coming down."

But declined to be more specific on Powell's even after repeated questions, saying he'd "do whatever is necessary to make America great again."

Trump has previously said, as in a 2020 news conference, that "I have the right to remove" Powell and has also signaled that he'd attack any move to lower rates before the election as a political move from Powell to help Biden.

And a recent report in the Wall Street Journal found Trump allies have drafted a proposal that could severely undermine Fed independence and give the president a direct say in the setting of interest rates.

But for now, Spindel says that Trump's attacks are unlikely to change Powell's behavior. The former president is already floating possible successors to Powell.

"I think a lot of what Trump's attacks do is hurt the integrity and the credibility of the institution," Spindel says.

Pressure from the left

Influential Capitol Hill Democrats are also turning up their pressure with new letters to Powell.

The first came from Democratic Sens. Warren, Jacky Rosen, and John Hickenlooper. The second came from Sen. Sheldon Whitehouse, the Budget Committee chair, and Rep. Brendan Boyle, the House's top Democrat on the issue.

Both focused heavily on the costs of housing as they made their case to Powell to lower rates now.

"America is also currently facing a housing supply crisis," Whitehouse and Boyle wrote, saying "high interest rates exacerbate this supply crisis by increasing the costs to develop new housing while discouraging existing homeowners from upgrading to larger homes."

The case from Biden's allies — which been echoed by a range of figures including at least one former Trump economic advisor — is that high interest rates make the inflation problem worse when it comes to the housing context.

"It's becoming a vicious cycle and where Chair Powell thumps the housing market and comes back again and says we need more data," charged Bilal Baydoun, the director of policy and research at the left-leaning Groundwork Collaborative.

Baydoun says Powell needs to change course but worries he won't because of politics and "a fear of being perceived as tipping the scales."

Biden has been more circumspect but also commented on the Fed in the context of housing. "I bet you that that little outfit that sets interest rates is going to come down," Biden said in a March speech while discussing mortgages.

It's a prediction he's repeated multiple times in the months since.

Chances for a 'pretty boring' June gathering

Powell might be able to stay out of the fray of politics this week but it could become a tougher job as the summer wears on.

Morningstar chief US market strategist David Sekera told Yahoo Finance Live this week that the gathering could be "pretty boring" but a rate cut on the eve of the election in September is still very much a possibility.

"I think they're going to want to give that indication to the market at the July meeting," he said.

Traders are currently projecting the chances of a rate cut before election day as essentially a coin flip. A tool that projects trader's views, as of Tuesday afternoon, projects a 49% chance of no easing between now and the September meeting.

It's a different story when it comes to the end of the year with traders projecting a nearly 87% chance of some easing before the dawn of 2025.

Lachman predicts that Powell will let in as little political noise as possible when he speaks to reporters this week.

"I think that he'll ignore it" and instead focus on the technical aspects of the Fed's work, he said. "He's pretty skillful at that."

But how Powell explains his position when the subject turns to the housing market will likely be closely scrutinized for months to come.

Baydoun says Powell "needs to explain" his approach to that issue. He adds housing is fundamental to how Americans see their future and "I'm fairly confident that the frustration over housing in particular will lead to more scrutiny."

Ben Werschkul is Washington correspondent for Yahoo Finance.

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