Is there a way to get from the McLauren airport to the Golden Nugget downtown without a $45 cab ride?

Besides telling the cab drivers to go a specific way so you don't get long hauled there is no way to reduce the price of a taxi. The only other way would be to take a shuttle or the city bus. I don't recommend walking as it will be a good seven miles or so.

From the Golden Nugget website:

Do you offer shuttle transportation to and from the airport?

Yes actually, we have partnered with Airlines Shuttle Corporation (ASC) to provide our guests with an exclusive non-stop direct shuttle service to and from McCarran Airport. All guests arriving at McCarran Airport Terminal 1 will exit Door 8 (eight) from baggage claim and Terminal 3 will exit Door 51 (fifty-one) from baggage claim. Roundtrip from McCarran or GNLV is $18.00. One way from McCarran is $9.00 + $1.00 airport fee = $10.00. Our bell desk can also set up a shuttle for your return trip to the airport, but they do need a 24 hour notification. There are also taxi cabs that can drop you off at the front doors of the Golden Nugget. Taxi rates vary but on average cost approximately $40 for up to 4 people.

http://www.goldennugget.com/LasVegas/faq.asp

If you take the WAX bus to 4th and Carson you will be in the Fremont Street area. From there it would be a short walk down Carson to Casino Center Drive (about 5 minutes) to the Golden Nugget. However, if you would like to take a taxi from here you would have to get to the nearest hotel. Taxis will not pick you up along the street like in NYC.

http://www.rtcsnv.com/wp-content/uploads/routes/20...

Yes. There is the WAX (Westcliff airport express) city bus. It departs from the ground level of either terminal. Follow the signs. Its 2 bucks maybe a tad more. Its almost all express, runs every half hour at most times and drops off right next to the golden nugget

Its McCarran

And the GN has a direct, non-stop shuttle from the airport to the hotel for $18 RT or $10 one way. If you arrive at Term 1, exit Door 8 at Baggage Claim. If you arrive at Term 3, exit Door 51

You can walk. Have any friends in Las Vegas, have them pick you up. If you can afford this trip I fail to understand why you cannot pay the cab ride.