In a speech to the Scottish Conservative conference, the prime minister insisted his party was the only one that could challenge the Nationalists.
He also described what he saw as the SNP's "litany of failure" in power.
Opinion polls suggest the Conservatives are in a race with Labour for second place ahead of May's Holyrood election.
The SNP is widely expected to secure a second successive majority in the Scottish Parliament in the election on 5 May, with the party having also formed a minority government between 2007 and 2011.
The Nationalists won all but three of Scotland's 59 seats at Westminster in last year's general election, with Labour, the Conservatives and Liberal Democrats winning just one seat each.
In his speech to delegates at the one-day conference in Edinburgh, Mr Cameron claimed Labour's "collapse" in Scotland meant the country was "in danger of becoming a one-party state".
He added: "We are the party that can challenge the SNP - now the only party that can challenge the SNP.
"They've been in power for nine years - they are the establishment."
He highlighted "stagnating" school attainment figures, "falling" numbers of college students, "cuts" in the help for poorer university students and "unfulfilled" spending on the NHS as being among the SNP's "litany of failure" in government.
The PM went on: "There's even the absurd Named-Person policy, which ensures every child is allocated a guardian - even if they have parents; even if they have no need for this extra layer of bureaucracy.
"Well I'll tell you who needs a guardian - someone to keep them in check - it's the SNP.
"And it falls to us, the Conservatives, the only party fit to expose these spendthrift, out-of-touch, dogmatic, inept Nationalists for what they really are."
The conference will also hear from Defence Secretary Michael Fallon, who is expected to renew his attack on Labour over its divisions on Trident.
And Scottish Conservative leader Ruth Davidson will call on the SNP to commit to a new NHS funding guarantee in her address to delegates.
Ms Davidson will say NHS budgets should increase by the higher of either 2% or all of the additional Barnett formula funding to Scotland, as a result of increased spending on the NHS in England.
She will also say that health spending in Scotland increased by only 1% in real terms between 2010 and 2015, compared with a 7% rise in England.
Ms Davidson will stress that most patients have a good experience of the NHS, and will describe how she recently met a retired surgeon who she credits with saving her life at the Sick Kids hospital in Edinburgh when she was hit by a truck at the age of five.
But she will say that the pressures in areas such as general practice and recruitment are only getting more intense, and will accuse the SNP of "failing to care" for the NHS during its time in government.
And she will add: "There is no way around this: if we want to maintain our NHS to the standards we rightly expect, then increased spending must be part of the solution."
Only the Tories can challenge the SNP and prevent Scotland becoming a "one party state", David Cameron has said.