The United States has recently been in talks with the government of Saudi Arabia over the issue of nuclear technology. The Saudi government has been seeking the technology from the US, which it claims is solely for use by the civilian energy sector. However, they have refused multiple requests by the US to comply with comprehensive nonproliferation rules, such as allowing IAEA inspections and the gold standard, which requires that they would not enrich uranium to weapons-grade levels. None of these restrictions would materially impact civilian use of nuclear power.
This demonstrates that the Saudis are likely seeking out nuclear technology for the development of nuclear weapons. Given the proxy conflict between Saudi Arabia and Iran, it is not outrageous to believe this. Obtaining nuclear weapons would give the Saudis the edge over the Iranians in the situation a conflict did break out. Crown Prince Muhammad bin Salman has even publically stated that Saudi Arabia will pursue acquiring nuclear weapons if Iran develops them.
The potential that Saudi Arabia acquiring nukes would cause instability and regional conflict is incredibly high. Acquiring nuclear weapons would embolden Saudi Arabia to further encroach upon the sovereignty of its neighbors, which it is already notorious for (see the ongoing conflict in Yemen). It would lead to more direct military action against their enemy, Iran, and further fracturing of the region, as it is caught in the crossfire. This would inevitably lead to an increase in radical islamic terrorism, as the Saudis further arm and fund proxy groups, which are largely radical Wahhabi extremists.
The Saudis obtaining nuclear weapons would also put an end to the JCPOA (The Iran nuclear deal), as the Iranians seek to achieve parity. This would allow Iran to restart development of nuclear weapons, which they have currently ceased. Both Saudi Arabia and Iran acquiring nuclear weapons would be a worst-case scenario.
If both nations obtain nukes, the fallout (pun intended) would be immense. The possibility of nuclear war in this century would greatly increase. An attack on one country by a proxy group of another, such as what happened just recently with the drone attacks against Saudi oil facilities by the Houthi rebels in Yemen, could easily escalate to nuclear war. Israel is already armed with nukes as well and would likely be dragged into any potential conflict, especially if it went nuclear.
A nuclear war in the Middle East would be utterly devastating. It could potentially kill tens of millions of people and make swathes of land uninhabitable. For these reasons, I would argue that US Senators Ed Markey and Jeff Merkley are absolutely right to oppose this action by the current administration.