Mitt Romney’s sweeping victory in the Florida Republican primary Tuesday did two things for him that he badly needed: It set the front-runner back on a glide path to the 2012 presidential nomination, and it raised his standing with the GOP’s conservative base.

Florida, the fourth state to vote this primary season, was not only the biggest prize yet, but also the purest test of where the party stands nationally.

Unlike earlier primaries in New Hampshire and South Carolina, Florida’s contest was open only to registered Republicans; about seven in 10 voters identified themselves as somewhat or very conservative, according to exit polls.

Though Romney’s victory could be a turning point, senior Republicans say the race for the nomination is far from over.

“Florida is a big and diverse state that will be a crucial state in the fall. This is an important win for Romney,” said Ralph Reed, head of the Faith and Freedom Coalition, a conservative Christian political organization. “But given all the ups and downs we’ve had, I don’t think you can call this for Romney just yet.”

The size and breadth of Romney’s win provide the first real evidence that he has the potential to coalesce a party that has been deeply split between its establishment wing, which backs him, and the insurgent forces of the tea party movement, which have been suspicious of his moderate record.

The result in Florida was very different from the defeat Romney suffered in South Carolina only 10 days before.

In Florida, Romney was competitive with former House speaker Newt Gingrich among evangelical Christians. He also prevented Gingrich from running up the large margins he had in South Carolina among tea party supporters and the most conservative voters.

The win also gives Romney a shot of momentum going into February’s contests, most of which will be held on terrain where he has an advantage. Internally, Romney’s campaign is calculating that the primaries and caucuses this month could boost his delegate total to 250 or more, nearly a quarter of what he needs to nail down the nomination.

Still, there is likely to be tension going forward. In the exit polls, more than seven in 10 Gingrich supporters said they see Romney as insufficiently conservative, and more than half would be dissatisfied with him as the party’s nominee.

That’s a feeling that goes both ways: About six in 10 Romney supporters who were polled said they would be unhappy with Gingrich at the top of the Republican ticket.

But that breach may close once a nominee is chosen and Republicans turn their attention to the general election. As in earlier contests, a plurality of Republicans in Florida said the top quality they are seeking in a candidate is the ability to beat President Obama.

Florida — a swing state where the GOP will hold its national convention in August — also afforded the Romney campaign an opportunity to road-test some of its messaging for the general election.

For instance, Romney’s strategists closely watched his totals among women, a constituency where Republicans often have a disadvantage in the fall. In Florida, they were the key to Romney’s victory.

Among Florida Republican women, Romney beat Gingrich by more than 20 percentage points, according to exit polls. That was a sharp swing from South Carolina, where Gingrich ran nine points ahead of Romney among female primary voters.

One adviser, who spoke on the condition of anonymity so he could discuss campaign strategy frankly, said the Romney campaign’s attacks on Gingrich as unreliable and erratic were aimed squarely at winning Republican women.

This election season has been one of serial infatuation for Republicans across the country. At various points since August, three other candidates — first Texas Gov. Rick Perry, then former pizza chain executive Herman Cain and then Gingrich — have been ahead of Romney in the national polls.

So unsettled was the race that, for the first time, three different candidates — former senator Rick Santorum (Pa.), then Romney, then Gingrich — won the first three contests.

In the Florida exit poll, nearly six in 10 said they were satisfied with the field of candidates. But that feeling is not shared by Republicans nationally; indeed, as they have watched a campaign that has become increasingly bitter and bruising, there is evidence that they are growing more disenchanted with the choices.

In a Pew Research Center poll released Monday, 46 percent of Republicans and Republican-leaning voters rated the GOP field as excellent or good; 52 percent said it was poor or fair.

That was almost an exact reversal of how such voters felt shortly before the New Hampshire primary in early January. At that point, 51 percent thought favorably of the Republican candidates, and 44 percent thought them fair or poor.

And it represents a dramatic decline of 22 points from four years ago, when 68 percent said they liked the GOP field.

Yet for all their dissatisfaction with the options on the ballot, Republicans are turning up at the polls in record numbers.

“What we know for sure about Republican primary voters nationally is their level of interest matches the historic high-water mark of the 2008 election,” said GOP pollster Bill McInturff. “And this high interest and unprecedented campaign spending has led to historic levels of turnout in every caucus and primary so far in January.”

Polling director Jon Cohen contributed to this report.