Gov. Maura Healey of Massachusetts, a liberal Democrat, has declared a state of emergency, activated the National Guard and started petitioning the White House for help.

The migrants on state-funded buses from Texas are a fraction of the total number arriving in northern cities. Texas brags that its “Operation Lone Star” has sent more than 13,100 migrants to New York City since August 2022, but the overall strain there stems from the total, more than 110,000. Some of those migrants have family in New York, while others are attracted to the city’s history of welcoming immigrants.

Still, the rising clamor is creating a rare convergence between the two parties, which for years have fought in seemingly parallel political universes. Democrats focused on issues like abortion, the preservation of democracy and expansion of health care, while Republicans warned of a migrant “invasion” and railed against “woke” liberal ideology, socialism and expanding L.G.B.T.Q. rights. Endless Republican news conferences at the border and threats to impeach Alejandro Mayorkas, the homeland security secretary, were dismissed as political bluster.

Now, suddenly, some Democrats are sounding remarkably like Republicans.

“Upstate New Yorkers shouldn’t be forced to bear responsibility for decades of failed immigration policy, dysfunction and stupidity out of Washington, Albany and places like New York City,” said Josh Riley, the Democratic candidate seeking to unseat Representative Marc Molinaro, a Hudson Valley Republican. Mr. Riley added that it was time for Mr. Biden to “to step up and help out.”

For Republicans, the response to Mr. Abbott’s gambit has gone beyond what they could have hoped for — a spreading of the pain, as millions of migrants stream across the southern border, fleeing violence and poverty, drawn to what they see as a more welcoming administration in Washington and plentiful work.