BERLIN — Dozens of lawmakers from her own conservative party signed open letters against her this week. A nationalist right-wing party is gaining in strength. Speculation, building since the fall, now runs rife that she should even be replaced. On Sunday, the top circulation Bild Zeitung headlined an eight-page spread on her political troubles: “Is Merkel Still the Right One?”

After a year in which Chancellor Angela Merkel welcomed more than a million asylum seekers, that decision has left her more embattled and isolated, at home and in Europe, than perhaps at any other time in her 10 years in office.

It is a change that threatens not only Ms. Merkel’s position, but the cohesion of an already deeply troubled European Union, where her strength and that of Germany — the Continent’s No. 1 economy — has served as the linchpin for the 28-member bloc through more than a half decade of economic crisis.

“The state of leadership in Europe is such that the future of the E.U. currently rests on Merkel’s strength, or weakness,” said Constanze Stelzenmüller, a fellow at the Brookings Institution in Washington. “Last year, we thought Europe could unravel over the euro. Now, it could be border security.”