GEOFF BENNETT: Congress arrived back in Washington today with a long list of priorities for Speaker Mike Johnson to accomplish and a razor-thin margin to get it done.

Our Lisa Desjardins has this report.

LISA DESJARDINS: It's been a cold spring in Washington, beautiful, but, for the House of Representatives, delicate and uncertain, with echoing sounds that are the most daunting yet for the new House speaker.

REP. MARJORIE TAYLOR GREENE (R-GA): I will not tolerate a speaker of the House that I voted for to sell us out.

LISA DESJARDINS: Republican Congresswoman Marjorie Taylor Greene in a town hall in Tunnel Hill, Georgia, last night again made it clear she wants Mike Johnson out.

REP. MARJORIE TAYLOR GREENE: I will not tolerate this anymore.

LISA DESJARDINS: Greene has filed a potent bill, just one sentence declaring the speakership to be vacant, in other words, removing Johnson.

She's not yet forcing a vote, but it's a threat... MAN: The bill is passed.

LISA DESJARDINS: ... one issued last month after she and scores of Republicans broke with Johnson over the compromise deal to keep government funded.

REP. CHIP ROY (R-TX): That is not the way to do business.

LISA DESJARDINS: Beyond spending, Johnson has other dilemmas.

There's the border.

Conservatives decry a lack of progress, though nothing can pass both chambers right now.

There's FISA, the Foreign Intelligence Surveillance Act.

Key powers are expiring next week, and Republicans are divided.

Then there's Ukraine and Israel, with increasing calls for conditions on Israel aid.

And if Johnson proposes Ukraine funding, he risks direct fire from a large group in opposition.

FMR.

REP. JOHN FLEMING (R-LA): He's really kind of standing at the dike trying to plug holes right now, so I have tremendous sympathy for my good friend Mike Johnson.

LISA DESJARDINS: John Fleming is now the treasurer of Louisiana, but over a decade ago, he was part of the Tea Party movement and a founder of the Freedom Caucus.

He defends the sharp motion to vacate.

FMR.

REP. JOHN FLEMING: I think Democrats, to their credit, they fight.

Even when they're underdogs, even when they're in the minority, they fight hard for their policies.

I can't say that about Republicans.

Republicans oftentimes give in way too quickly.

LISA DESJARDINS: But the problem for Johnson is that he has some members who want to fight, but he has a bare majority.

He doesn't have room to maneuver, nor does he have good troop morale.

REP. MIKE JOHNSON (R-LA): We're living a time of divided government.

Democracy is messy.

Sometimes, it's very messy.

This is part of that process.

And we're going to keep steady hands at the wheel.

LISA DESJARDINS: Republicans like Marjorie Taylor Greene do not want steady.

They want their way.

And she's using the tight margin in the House right now to try and get it.

In just over a week, that vote gets even one vote tighter.

That means, to pass nearly anything, including Ukraine funding, it must be bipartisan.

However, if Johnson pushes bipartisan bills, it would take just two or three Republicans to take away the majority from him as speaker.

Democrats could help him survive with their votes, but that would spark another major problem.

FMR.

REP. ERIC CANTOR (R-VA): I think it's a really, really untenable spot to be put in to be propped up by the opposition.

LISA DESJARDINS: Eric Cantor is a former House majority leader who lost to a Freedom Caucus opponent.

He says, if Johnson survives thanks to votes from Leader Hakeem Jeffries and other Democrats, that would undermine Republicans running in primaries across the country.

Cantor also sees the problem Johnson faces against all-or-nothing tactics from within the party.

FMR.

REP. ERIC CANTOR: I think that's really important to never, ever sit here and just throw your hands up and say, we're going to be part of the destruction caucus and never get anything done.

LISA DESJARDINS: You used the phrase destruction caucus.

FMR.

REP. ERIC CANTOR: For some, there is, and they have been quoted as such, saying nothing that Washington does is good.

And I sort of questioned to myself, how is it that you want to be elected and serve in Washington if you say it's all bad?

LISA DESJARDINS: For Speaker Johnson, who may control the fate of Ukraine aid, FISA reauthorization and most any issue in Congress at the moment, the question is, can he find a way to get anything done and also survive?

For the "PBS NewsHour," I'm Lisa Desjardins.