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Republican lawmakers return to the Capitol this week after the unexpected death in office of Lindsey Graham, as the party seeks to appoint a new senator to see out his term.

Lawmakers from both parties are eager to highlight before voters legislative victories ahead of the midterms, where control of Congress is at stake.

But for Senate Republicans, who are already navigating an array of demands from Trump, their agenda grew further complicated over the weekend with the death of Lindsey Graham, the budget committee chair who is a key player in negotiating a party line bill to fund additional defense spending and other priorities outlined by the president.

South Carolina governor Henry McMaster is tasked with appointing a new senator to serve out the remainder of Graham’s term, which ends on 3 January. The appointment is expected to be announced in a matter of days.

Whoever is chosen will likely have a leg up in a special primary election on 11 August to fill Graham’s place on the November ballot, which he won despite facing five challengers from his party in June.

The candidate would still run against Democratic nominee Annie Andrews, a pediatrician who gained significant support in the red state, but still faces an uphill challenge.

It means that together with the ongoing absence of Mitch McConnell for unexplained health issues, Senate Republicans will have to navigate a majority that’s down two members.

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The Senate judiciary committee has scheduled two days of confirmation hearings for Todd Blanche, the acting attorney general Trump has nominated to the post, though it was unclear if the death of Graham, who served on the committee, will affect the schedule. The intelligence committee has separately announced that the confirmation of Clayton is back on.

Republicans in both chambers remain confounded by Trump’s renewed fixation on the Save America Act, which would ban mail-in ballots and impose new rules on voting nationwide. The measure, a version of which was approved by the House of Representatives earlier this year almost entirely with Republican votes, has no path through the Senate, where it faces opposition from Democrats and some in the GOP.

Ro Khanna accused the Israeli government and military of “lying” on Sunday about the US congressman’s detention by armed settlers and Israeli soldiers during a recent visit to the Israeli-occupied West Bank. Khanna – a California Democrat – had posted video evidence on social media of Israeli settlers and soldiers blocking the path of his convoy on Wednesday in the South Hebron hills, near the village of Zanuta, where Israelis have driven Palestinians from their homes in what Amnesty International calls a government-backed “ethnic cleansing campaign”.