The US Senate on Thursday blocked two bills, including one piece of legislation backed by President Donald Trump, that were aimed at ending the record-long partial federal government shutdown.

The first was a Republican bill that included Trump's border wall funding and temporary protections for young undocumented individuals brought to the US as children.

The second was a Democratic bill that would have funded the government for three weeks, but did not include the wall funding that Trump wants.

Trump last month triggered the shutdown, now in its 34th day, by demanding $5.7bn for a US-Mexico border wall, which is opposed by Democrats, as part of any legislation to fund about a quarter of the government.

The longest such shutdown in US history has left 800,000 federal workers as well as private contractors without pay and struggling to make ends meet, with the effects on government services and the economy reverberating nationwide.

Possible compromise

The mere fact that Senate Majority Leader Mitch McConnell was willing to allow a vote on the Democratic bill suggests he may be trying to persuade lawmakers from both parties to compromise. He had previously said he would not bring any bill to the floor that Trump would not sign.

The Republican-backed bill would have provided wall funding and a temporary extension of protections for "Dreamers", hundreds of thousands of people brought to the United States without documents as children. Trump offered the deal on Saturday.

But Democrats have dismissed Trump's offer, saying they would not negotiate on border security before reopening the government and would not trade a temporary extension of the immigrants' protections in return for a permanent border wall they have called ineffective, costly and immoral.

Analysts believe that McConnell's decision to call the votes may signal that he may be trying to convince Republicans and Democrats to seek a compromise.

One possibility emerged on Wednesday when House Democratic leaders floated the idea of giving Trump most or all of the money he seeks for security along the Mexican border but that could not be used to build a wall.

Drones, sensors and X-rays

Representative James Clyburn, the third-ranking House Democrat, said Democrats could fulfil Trump's request for $5.7bn for border security with technological tools such as drones, X-rays and sensors, as well as more border patrol agents.

On Wednesday, House Speaker Nancy Pelosi, the top US Democrat, essentially disinvited Trump from delivering the annual State of the Union address in the House chamber until the government is fully open. Trump initially called her move "a disgrace", before acquiescing in a late-night post on Twitter.

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"I will do the Address when the Shutdown is over. I am not looking for an alternative venue ... because there is no venue that can compete with the history, tradition and importance of the House Chamber," he wrote. "I look forward to giving a 'great' State of the Union Address in the near future!"

Pelosi responded on Twitter with a call to Trump to support House-passed legislation to end the government shutdown. "Please accept this proposal so we can re-open government, repay our federal workers and then negotiate our differences," she said.

A Reuters/Ipsos poll last week found that more than half of Americans blamed Trump for the shutdown even as he has sought to shift blame to Democrats after saying last month he would be "proud" to close the government for border security.