MILWAUKEE — Worried about the potential impact on the fragile economies in their states, Republican governors this weekend warned their counterparts in Congress not to shut down the federal government as part of an effort to block financing for President Obama’s health care law.

A range of Republican governors, including some who have refused to implement elements of the health initiative in their states, said in interviews that a standoff in Washington before the new fiscal year this fall could backfire on the party if it is seen as being responsible for bringing the government to a halt.

“I have made the case that Obamacare is not good for the economy, but I have some real concerns about potentially doing something that would have a negative impact on the economy just for the short term — I think there are other ways to pursue this,” said Gov. Scott Walker of Wisconsin, who hosted about half of the country’s governors here for the summer meeting of the National Governors Association.

Gov. Jack Dalrymple of North Dakota said a government shutdown would invariably be blamed on the legislative branch.