This week will be the last chance for the US Senate to vote on a bill that would see Irish workers being given access to thousands of US visas every year.
Ireland wants to be added to the E-3 visa programme which is currently only available to Australians, something which requires the US Congress to pass legislation.
Last month, the House of Representatives voted in favour of the bill but it needs to be passed unanimously by the US Senate.
Six Republican senators had put a hold on the bill, but last week that number had been reduced to just one senator.
This is the last week of the current US Congress, which means if the bill is to become law it must be passed by the Senate in the coming days.
Over the weekend, the conservative right-wing news website Breitbart ran a negative article about the bill, saying it would "outsource many thousands of US college graduate jobs to Irish graduates and deliver amnesty to Irish illegals".
While the Irish Government is looking at ways of helping undocumented migrants, the E-3 visa programme is unlikely to benefit them.
Separately, a Democratic Senator appeared to criticise Speaker of the House Paul Ryan for his involvement in the bill.
Brian Schatz wrote on Twitter: "Paul Ryan is still the Speaker of the House and they are out of session until Wednesday, with shutdown looming Friday. But, in his defense he IS (checks notes) working on getting more (checks notes again to make sure) people from Ireland into America. Seriously he is doing that."
Paul Ryan is still the Speaker of the House and they are out of session until Wednesday, with shutdown looming Friday. But, in his defense he IS (checks notes) working on getting more (checks notes again to make sure) people from Ireland into America. Seriously he is doing that.— Brian Schatz (@brianschatz) December 15, 2018
Every year, more than 10,500 E-3 visas are offered to Australians who want to work in the US but only about half of them are taken up.
Ireland wants to be able to access the remaining unused visas.
The Irish Government is working on a reciprocal arrangement which would ease restrictions on US citizens who wish to retire to Ireland and enable US citizens to work in Ireland on a similar basis.
The issue of immigration was raised by Taoiseach Leo Varadkar during his meeting with US President Donald Trump at the White House in March.
Efforts to gain access to the E-3 visa programme have been led by the Government’s special envoy to the US - Fine Gael TD John Deasy - and by the Irish Embassy in Washington.
E-3 visas are for two years but can be renewed indefinitely.
They allow the spouses of recipients to work in the US but not their children.
To qualify, applicants must be employed in a specialty occupation, have a legitimate offer of employment in the US and possess the necessary academic or other qualifying credentials.