WASHINGTON (NYTIMES) - United States President Donald Trump said late on Wednesday (Jan 23) that he would deliver his State of the Union address once the federal government reopens, capping a day of brinkmanship with Speaker Nancy Pelosi, who told the President that he was not welcome to deliver the speech in the House chamber while the government is partly closed.

Shortly after 11pm, hours after he said he would look for another venue for the speech, Mr Trump wrote on Twitter: "As the Shutdown was going on, Nancy Pelosi asked me to give the State of the Union Address.

"I agreed. She then changed her mind because of the Shutdown, suggesting a later date. This is her prerogative - I will do the Address when the Shutdown is over."

The President's seeming capitulation came even as House Democratic leaders said they were prepared to give him a substantial sum of money for border security - perhaps even the US$5.7 billion (S$7.7 billion) he has requested - but not for a wall and not until he agreed to reopen the government. That figure is roughly double what Democrats had previously approved.

On the other end of the Capitol, in the Republican-controlled Senate, lawmakers prepared for crucial votes on Thursday on two competing proposals - one backed by Mr Trump and Senate Republicans, the other by Democrats - that would bring an end to the partial shutdown, though neither might garner the 60 votes necessary for passage.

On Day 33 of the longest government shutdown in history, Washington took on the air of a split-screen television.

On one side was a spat between Mr Trump and Ms Pelosi - a powerful man and an equally powerful woman - over the President's constitutional duty to periodically report to Congress on the state of the union.

On the other, the House and Senate trudged along with their daily business, with lawmakers in both parties grasping for a way out of the shutdown stalemate.

It now seems all but certain that 800,000 federal employees who have been either furloughed or working without pay for more than a month will miss another pay cheque on Friday. The best hope, people in both parties say, is that the expected failure of both Bills in the Senate on Thursday will prompt bipartisan negotiations that could lead to a compromise.

Those Bills take very different approaches. Mr Trump's Bill would include US$5.7 billion for the wall and extend protections to some immigrants in the country illegally - protections that he himself revoked - while sharply curtailing access to asylum.

The Democrats' measure would simply fund shuttered government agencies through Feb 8, with no wall money.

But with the House set to leave town on Thursday, it is highly unlikely that the impasse will end by next Tuesday, when Trump is scheduled to deliver his address, an annual Washington ritual that usually plays out with pomp in front of both chambers of Congress, the Supreme Court, Cabinet secretaries and honoured guests.

For Mr Trump, it would be a moment to command the stage - with television cameras rolling and Ms Pelosi stuck behind him, trying to figure out whether to grimace or nod.

Now, the President is trying to paint Ms Pelosi as a left-wing radical who cancelled the address for political reasons, despite her assertion that she simply wanted to postpone, not cancel, it because of the burden it would impose on Secret Service agents working without pay.

"It's really a shame what's happening with the Democrats," Mr Trump told reporters at the White House. "They've become radicalised."

In the afternoon, Mr Trump pledged to "do something in the alternative", and it was not clear at the time whether he had completely given up on holding the speech in the Capitol.

Some lawmakers raised the possibility that he could deliver it in the Senate chamber. But others, as well as some Trump advisers, suggested it would be better for him to issue the speech at the border or during a rally.

But ultimately, the President wrote on Twitter, he decided against an alternative site "because there is no venue that can compete with the history, tradition and importance of the House Chamber".

He added: "I look forward to giving a 'great' State of the Union Address in the near future!"

While the President is permitted on the floor of the House, he needs an invitation to speak.Ms Pelosi had invited Mr Trump to deliver the speech in a letter on Jan 3, when she was sworn in as Speaker.

But in a second letter on Jan 16, she warned that there were security concerns, and asked that they "work together to determine another suitable date after government has reopened", or that Mr Trump consider delivering it in writing.

On Wednesday, Mr Trump called Ms Pelosi's bluff, with a letter saying that he had checked, and that the Secret Service had no such concerns. So he said he was accepting her initial invitation.

Republican lawmakers piled on. The House Republican leader, Mr Kevin McCarthy of California, released a video on Twitter of him signing the resolution formally inviting the President to the House.

"Retweet if you agree that the State of the Union should proceed as planned," Mr McCarthy wrote.

But hours later, Ms Pelosi fired back with a letter of her own, telling the President she would not pass a resolution authorising him to come until the government had reopened.

As the two traded barbs, House Democrats passed yet another in a string of spending Bills that would reopen the government; this latest one included US$1.5 billion in border security and was based on measures that gained approval from both parties in the last Congress.

During a closed-door meeting with House Democrats on Wednesday morning, Ms Pelosi urged her caucus to stay unified and not to peel off and begin negotiating with the President on his terms, which could muddle the stark differences between Mr Trump and them on a critical issue.

She also told rank-and-file lawmakers that they should not get "too bogged down" on what legislation was being voted upon - a direct message to some of her restive centrist freshmen, who have been meeting Republican freshmen to discuss a bipartisan path out of the shutdown.

The appeal seems to have worked; as they emerged from the closed-door meeting, rank-and-file Democrats appeared united behind their leaders' demand that the government open before border security negotiations took place.

"There's an overwhelming consensus that this is about establishing that shutdowns are wrong," said one centrist, Democratic Representative Tom Malinowski. "From my standpoint, and I think this is the consensus of the caucus, everything is negotiable. Border security is negotiable. Immigration policy is negotiable. Shutting down the government is not negotiable, and we're angry about it."

He went on: "If we give in to this tactic in any way we will validate it, and there will be no end to these shutdowns, and the people who suffer today will be suffering again and again and again. We cannot have that."

House Democrats are also drafting their own plan for border security, which is expected to be made public in the coming days. "We are going to be talking about substantial sums of money to secure our border," Democratic Representative Steny Hoyer, the majority leader, told reporters.

Representative James Clyburn of South Carolina, the No. 3 Democrat, said separately that Democrats could back a US$5.7 billion funding measure that included drones and refitted ports of entry - but no wall. That is the amount Mr Trump has demanded for the wall he wants to build on the south-western border.

"Using the figure the President put on the table, if his US$5.7 billion is about border security, then we see ourselves fulfilling that request, only doing it with what I like to call using a smart wall," he said.

Both Mr Hoyer and Representative Hakeem Jeffries of New York, chairman of the House Democratic Caucus, seemed to leave the door open for eventual negotiations to include talk of some kind of border barrier - so long as the government was open first.

When asked point-blank if Democrats would agree to talk about a wall, Mr Jeffries did not say no but reiterated Democratic talking points about what the party favours: new scanning technology to detect drugs and weapons, improvements in infrastructure at ports of entry and more personnel, including more immigration judges.

Mr Hoyer was asked whether Democrats might consider permanent protections for the young immigrants in the country illegally, known as Dreamers, in exchange for "some new physical barriers".

He said it was clear that Mr Trump would put money for a wall on the negotiating table.

"It's clear what the President wants; it's clear what we want," he said. "If you have a negotiation, both parties are going to put on the table what they want."