WASHINGTON — Justice Antonin Scalia’s death has given President Obama a tantalizing opportunity to reshape the Supreme Court, but cementing a lasting legacy on American jurisprudence will present a familiar challenge: breaking the will of Republicans.

On Monday, Senate Republicans — including some who are up for re-election in swing states — appeared to be closing ranks with Senator Mitch McConnell of Kentucky, the majority leader, who has vowed to block any nominee from Mr. Obama and has said that he should not even suggest one, leaving the choice to the next president.

Senator Rob Portman, Republican of Ohio, who faces re-election this year, backed that position on Monday. “It is common practice for the Senate to stop acting on lifetime appointments during the last year of a presidential term, and it’s been nearly 80 years since any president was permitted to immediately fill a vacancy that arose in a presidential election year,” he said in a statement. Senator Pat Toomey, Republican of Pennsylvania, who also faces re-election, said he, too, backed a delay.

Senator Kelly Ayotte, Republican of New Hampshire, who faces a primary threat from the right wing of her party, said over the weekend that she supported Mr. McConnell. And several conservative groups have begun to mobilize around the issue, which is already animating activists.