Plenty of Republicans are itching to start the year’s second big Cabinet confirmation fight over putting Tom Perez in charge of the Labor Department. They’ll be pressed hard to back away from such a confrontation after pondering the autopsy and re-branding report from their national party organization, meaning the second-term Obama Cabinet will have its first Latino member before Memorial Day.

The Republican National Committee’s endorsement of an immigration overhaul today, and its announcement that it will spend $10 million in the coming year on grass-roots outreach to Hispanics and other minority groups, is the party’s most assertively ambitious effort in a couple of decades to change its image after an electoral drubbing. But a big piece of the public relations benefit could be lost at the starting gate if the party’s congressional wing decides to make a big deal out of opposing someone who so clearly looks just like what the GOP says it wants to look more like.

Obama formally announced the Perez nomination today. But it’s been a done deal for the past week, allowing plenty of time for conservative groups and their GOP allies in the Senate to start building their paper trail against him — mainly focused on his past three and a half years as head of the civil rights division at the Justice Department.

Some don’t like his office’s work to stop South Carolina and Texas from setting new voting rules that his team viewed as racially biased. Others don’t like Perez’s several confrontations with Joe Arpaio, the immigration hard-liner Arizona sheriff. Iowa’s Charles E. Grassley, the top Judiciary Committee Republican, is particularly irked that Perez backed away from a lending discrimination lawsuit in Minnesota. And most problematic of all for the nominee, in the eyes of the GOP, is a Justice inspector general’s report released last week that suggests Perez has done too little to combat “deep ideological polarization” in his division’s voting rights office.

But none of those criticisms appears, at least so far, to have the sort of staying power and sound-bit strength to become the basis for a viable GOP filibuster, or even to slow down the scheduling of a confirmation hearing for very long. In part, that’s because none of those matters has to do with the sort of issues that Perez would tackle at Labor. His record on that score mainly comes from his two years as Maryland’s secretary of Labor. (That record helped prompt 22 Republicans, 17 of whom are still in office, to oppose Perez’s 2009 confirmation to his current job.)

Instead, much of the Perez debate is destined to become about immigration, since the Labor Department would have a significant role in implementing the comprehensive overhaul measure now gestating at the Capitol. The nominee is likely to  be pressed hard to detail his views about two provisions that both sides see as essential components of a broad bill: A new and reliable immigration-status verification system for potential employers to check, and a new guest worker program for low-skilled immigrant laborers that both protects American laborers but helps business meet their demand for lesser-skilled workers.

On these fronts, Republicans hoping to heed the messages of today’s Reince Priebus report will want to give Perez wide latitude, which probably means saying little in his own coming testimony that might complicate any back-channel negotiations toward a bipartisan compromise that are still underway.

Beyond that — if they want to shed their newly acknowledged image as the party of “stuffy old men” — they will be hard pressed to get out of Perez’s way altogether.