The Mayor of Boston has said he could not back a special deal for the undocumented Irish in America despite being "a proud son of Irish immigrants".
Marty Walsh, whose parents come from Galway, has been one of the most vocal critics of Donald Trump's immigration policy.
During a meeting with Enda Kenny yesterday he asked the Taoiseach to bring a strong message to Washington on Thursday that Americans want "a solution instead of accusing folk of people illegal and being criminals".
Mr Kenny has said he will prioritise the 50,000 illegal Irish during his White House visit and "a strong case on behalf of the hard-working, tax-paying Irish people in the US who for too long now have been living in the shadows".
However, Mr Walsh suggested the conversations should be much broader than just the Irish situation.
"I'm a proud son of Irish immigrants, but I would not be supportive of rules and regulations that just benefit people who are undocumented Irish.
"We need a comprehensive piece of legislation, we need some clarity for all immigrants, all undocumented immigrants," Mr Walsh said.
Mr Kenny said he accepted "it's not just about the Irish".
"Clearly, Ireland has a long history with the US over the last 200 years and the contribution made by Irish immigrants and their descendants speaks for itself," he said. "With 11 million undocumented people living in the US, what is needed is a pattern of reform and we've discussed how that might actually apply."
President Trump's new executive order restricting immigration rights to citizens of six predominantly Muslim countries takes effect on the same day that he meets Mr Kenny for the traditional St Patrick's Day shamrock ceremony.
The Taoiseach said: "It is not for me to comment on executive orders, but in working with this new administration clearly we have some concerns and anxieties with regard to undocumented people living here.
"Not just in the case of Ireland, but also containing many others. It's not a case of picking and choosing."
Mr Walsh said he was "not heartened at all" by the introduction of more immigration restrictions.
"Hopefully the Taoiseach will be able to help a little bit here, to have a conversation with the president and administration about how we come up with a solution instead of accusing folk of people illegal and being criminals.
"I can't stand here and say I feel comfortable where we are as a country, and yet I'm hoping that we move to that point, but not today," he said.