Republicans in Congress suffered a humiliating series of setbacks on Tuesday on critical elements of their agenda, turning the Capitol into a den of dysfunction that has left several major issues, including U.S. military aid to Ukraine and Israel, in limbo amid political feuding.
As Republicans in the Senate torpedoed a border deal they had demanded, the bid by their counterparts in the House to impeach Alejandro N. Mayorkas, the homeland security secretary, collapsed amid Republican defections.
Then came one last bruising blow. Minutes after Republicans fell one vote short of impeaching Mr. Mayorkas — a punishment the party has promised its base ever since winning the majority — the House defeated legislation they put forward to send $17.6 billion in military assistance to Israel. The measure fell to opposition from Democrats who called it a cynical political ploy to undermine efforts to pass a broader foreign military aid bill including Ukraine. They were joined by a clutch of hard-right Republicans, who opposed the measure because the money was not paired with spending cuts.
Taken together, the events that unfolded on Capitol Hill on Tuesday offered a vivid portrait of congressional disarray instigated by Republicans, who are bent on opposing President Biden at every turn but lack a large enough majority or the unity to work their will.
They have sought to kill bipartisan efforts to send more military aid to Ukraine and to forge a compromise to secure the border against an influx of migrants, proposing instead to help Israel only and to push for the removal of Mr. Biden’s top immigration official. The back-to-back defeats on Tuesday showed that while they are adept at thwarting action on critical issues, they are hard-pressed to address any.
The paralysis left the fate of aid to Ukraine and Israel in peril, closing off what had been seen as the best remaining avenue on Capitol Hill for approval of critical military assistance to American allies. A broad measure that includes both is expected to fail in a Senate test vote on Wednesday, raising immediate questions about whether Congress could salvage the emergency aid package — and if so, how.
And it amounted to a disastrous day for Speaker Mike Johnson roughly 100 days into his speakership, highlighting his razor-thin majority and the unwieldiness of his conference.
In a statement, Mr. Johnson blamed Democrats for opposing the aid to Israel, which he said sent a “rebuke to our closest ally in the Middle East at their time of great need.” He said Republicans had only unveiled an Israel aid bill devoid of spending cuts as “a major concession” given “the gravity of the situation.”
But he left the Capitol without addressing what appeared to be a calamitous miscalculation on the impeachment vote, which had been little more than a political exercise given that the Democratic-led Senate would be all but certain to acquit Mr. Mayorkas.
Instead of a show of Republican unity for impeaching Mr. Biden’s top immigration official, the vote devolved into an extraordinary scene of chaos on the House floor that highlighted G.O.P. disarray, as leaders scrounged for the support to push through the charges against Mr. Mayorkas but were thwarted by their tiny majority.
They vowed to try again as soon as Wednesday.
“House Republicans fully intend to bring Articles of Impeachment against Secretary Mayorkas back to the floor when we have the votes for passage,” Raj Shah, a spokesman for Mr. Johnson, wrote on social media.
Tuesday’s failure underscored Republican divisions over the impeachment. Three G.O.P. lawmakers opposed the resolution, warning that it would set a dangerous precedent of impeaching administration officials for policy differences.
In a dramatic denouement, Democrats brought out Representative Al Green of Texas, still in a hospital gown from having undergone emergency surgery, to vote against the bill after he had missed previous votes. That deadlocked the tally, dooming the impeachment effort, which required a simple majority to pass.
Hard-right Republicans were livid, and expressed bafflement that their leaders did not seem to know exactly what their vote count would be on a major vote.
“I would have thought that they would know that,” Representative Ralph Norman of South Carolina said. “It isn’t that hard.”
Mr. Norman laughed when asked how he could explain the vote to his constituents.
“The conservative base is going have a real problem with this,” he said. “And they should.”
Representative Marjorie Taylor Greene of Georgia, who has led the charge for impeaching Mr. Mayorkas, said she expected House G.O.P. leaders to hold the vote again in coming days after calling Representative Steve Scalise of Louisiana, the No. 2 Republican, back to Washington. Mr. Scalise had been away from the Capitol recovering from treatment for multiple myeloma.
Ms. Greene predicted that the Republicans who sunk the measure would “be hearing from their constituents.”
The dysfunction is set to continue on Wednesday in the Senate when Republicans are expected to block a bill tying a border compromise to aid for Israel and Ukraine, after most of their members — even those who led the charge to negotiate it — turned against the package that House Republicans refused to consider amid opposition from former President Donald J. Trump.
“Joe Biden will never enforce any new law and refuses to use the tools he already has today to end this crisis,” said Senator John Barrasso of Wyoming, the No. 3 Republican. “I cannot vote for this bill. Americans will turn to the upcoming election to end the border crisis.”
Kayla Guo and Luke Broadwater contributed reporting.