The US needs to agree a new spending bill before the financial year ends at midnight on Monday. But political divisions have resulted in a stalemate.
In Italy, Prime Minister Enrico Letta is to hold a confidence vote on Wednesday.
There are worries over the economic impact of a shutdown of the US government.
If the government does shut down on 1 October, as many as a third of its 2.1 million employees are expected to stop work – with no guarantee of back pay once the deadlock is resolved.
National parks and Washington’s Smithsonian museums would close, pension and veterans’ benefit cheques would be delayed, and visa and passport applications would be stymied.
Programmes deemed essential, such as air traffic control and food inspections, would continue.
Republicans are targeting President Barack Obama’s healthcare law, popularly known as Obamacare.
Early on Sunday, the Republican-run House of Representatives passed an amended version of the Senate spending bill that removed funding for the healthcare law.
US Senate Majority leader Harry Reid has vowed that his Democrat-led chamber will reject the Republican bill.
“Tomorrow, the Senate will do exactly what we said we would do and reject these measures,” said Adam Jentleson, a spokesman for Senate Majority Leader Harry Reid.
“At that point, Republicans will be faced with the same choice they have always faced: put the Senate’s clean funding bill on the floor and let it pass with bipartisan votes, or force a Republican government shutdown.”
Speaking for the president, White House spokesman Jay Carney said: “Any member of the Republican Party who votes for this bill is voting for a shutdown.” The president, he said, would also veto the Republican bill.
Meanwhile Italy’s financial markets were also hit by a deepening political crisis there.
Italian shares are down almost 2% and the euro fell to the lowest level since June against the Swiss Franc.
Italy’s 10-year bond yield – an indication of how much the government has to pay to borrow money – rose as high as 4.66%, the highest level in more than three months.
Prime Minister Enrico Letta plans to hold a confidence vote on Wednesday, to seek the backing of Italy’s parliament.
He was forced to make that move after five ministers from Silvio Berlusconi’s party stepped down at the weekend.
But those ministers have now given mixed signals as to whether they are actually leaving the government.
The crisis follows weeks of worsening ties between Mr Berlusconi’s party and Mr Letta’s grouping.
Mr Berlusconi’s People of Freedom (PDL) objects to a planned increase in sales tax, which is part of a wider government policy to reduce big public debts.
The government has also been struggling with a deteriorating economy.
It is forecast to shrink by 1.4% this year according to the national statistics agency.
The agency also estimates that unemployment will reach a record high of 12.3% next year.
Earlier on Monday, Worries over the US shutdown had hit Asian shares.
Japan’s Nikkei 225 index closed 2% lower, Hong Kong’s Hang Seng was down 1.5%, Australia’s ASX fell 1.7%, while South Korea’s Kospi shed 0.7%
“It is the fear of the unknown,” said David Kuo of financial website the Motley Fool. “No one knows what is really going to happen and markets don’t like uncertainty.”
“There is likely to be some reduction in US government spending, but we don’t know what areas are going to be affected.
“Until that is resolved, we are likely to see volatility in the markets,” he added.