Less than five weeks remain for Dan Liljenquist to make his case to Utah Republicans that six terms is enough for Sen. Orrin Hatch.

The former state Senator still has plenty of ground to make up to overcome the household name Hatch has made himself over the past 36 years. Despite entering the 2012 cycle vulnerable to a conservative primary challenge, the sense on the ground in Utah is that Hatch is far more likely than not to return to the Senate in 2013.

“I would say if the election were held today, Hatch would probably have a 15-to-20-point win,” state Senate President Michael Waddoups (R) said.

Luckily for Liljenquist, the primary is June 26. But time is running out.

It’s been a month since the Utah Republican convention, where Hatch narrowly missed securing the nomination among 4,000 locally elected delegates. With a broader primary electorate, his prospects should be even brighter.

The pace of the race is just now picking up. Both candidates are finally on the air, as is at least one outside group supporting Hatch. And former Alaska Gov. Sarah Palin (R) on Tuesday officially endorsed the longtime Senator over his young, conservative challenger — a development the Hatch campaign didn’t know was coming.

FreedomWorks has spent more than $700,000 so far in an effort to defeat Hatch, and the conservative, D.C.-based group is continuing to tap into its 15,000 members in the state to build a volunteer and paid ground operation on Liljenquist’s behalf. But the Club for Growth, which spent $1.7 million in the effort to oust Indiana Sen. Dick Lugar in a primary earlier this month, never engaged.

Kirk Jowers, director of the University of Utah’s Hinckley Institute of Politics, said there doesn’t appear to be anything on the horizon that’s going to significantly cut into Hatch’s lead.

“It’s hard to imagine the game-changer,” Jowers said. “That’s why you get a Sarah Palin jumping on and Club for Growth backing away, because it doesn’t look like there’s a real logical path for Liljenquist to win this one.”

Still, Hatch and his allies aren’t taking their foot off the gas. Utah nonprofit Freedom Path just dropped $60,000 to run a TV ad this week that favorably ties Hatch to fellow Utah Sen. Mike Lee (R), who was elected in 2010 and remains closely affiliated with the tea party. It’s the same ad the group first aired in July, a month before Rep. Jason Chaffetz (R) announced he was taking a pass on the Senate race.

The Hatch campaign, which has been on the air for more than a week, will be running various ads through the primary that focus on his potential chairmanship of the Finance Committee and, more than likely, the golden-ticket endorsement from Mitt Romney.

“We’re certainly not taking anything for granted and working just as hard as we possibly can,” Hatch campaign manager Dave Hansen said. “So we feel very good about where the race is.”

Lugar’s loss and the insurgent Senate campaign of Ted Cruz (R), a tea-party-backed candidate running in the May 29 primary in the Lone Star State, are why there is a lack of premature celebration. Palin backed Cruz over Lt. Gov. David Dewhurst (R), the establishment candidate who is expected to come in first in Tuesday’s primary but might face a runoff in July.

Hatch had a $3 million cash edge at the end of March. Liljenquist faces a difficult task in persuading Republicans to vote out a potential committee chairman who wields a 90 percent lifetime vote rating with the American Conservative Union. Richard Mourdock, who knocked off Lugar, was a statewide elected official, and no one would compare Hatch’s well-regarded campaign to Lugar’s.

“We’re in the same basic spot that Richard Mourdock was in with Sen. Lugar, and we feel like the momentum is coming our way,” Liljenquist said in an interview. “If people see me and get to know me, we’re going to win this race.”

Liljenquist’s first TV ad, launched this week for a $125,000 flight, calls out Hatch for agreeing to only one radio debate, something Hatch has been criticized for in newspaper editorials as well. Liljenquist said he’ll be on TV through the primary.

Russ Walker, national political director at FreedomWorks, said the grass roots in Utah are firing up. But he conceded it’s going to be more difficult to oust Hatch than Lugar and that name recognition has been the greatest obstacle.

“The struggle is introducing them to enough people that you begin to get that snowball effect,” Walker said on his way to the airport, en route to Utah. “We kind of reached that critical mass in Indiana. We’re going to get there in Texas. I’m hopeful we can get there in Utah as well.”

The X-factor, Walker said, is Romney. Not only does the presumptive Republican presidential nominee’s endorsement carry a huge amount of weight in Utah, Romney’s name will actually be on the ballot.

“Hatch has made a really big deal about the endorsement, and they’ve run a lot of media featuring Romney endorsing Hatch,” GOP consultant LaVarr Webb said. “Just the fact that they’re on the ballot together probably helps Hatch a little bit.”

Jeff Hartley, a Utah lobbyist and former state GOP executive director, said Hatch is certainly the favorite, but the result will depend on whether Liljenquist can make stick the argument that Hatch has simply been in Washington too long.

“It could — it has in a lot of races around the country in the past,” Hartley said. “It happened when Hatch was first elected. But it has to be done the right way.”