Nevada, New Mexico and Colorado were won by Bush in 2004 and are considered tight enough to be won by either candidate and help clinch the presidency.
Some polls say that Obama, 47, holds a slight lead in Nevada, which Bush won by less than one per cent in 2004, and New Mexico.
On Saturday, the Illinois senator thanked people for the outpouring of support over his grandmother's illness.
"I just want to personally say how grateful I am that so many people sent out their thoughts and prayers sent my grandmother flowers, get well cards," he said.
In an interview with ABC News, broadcast on Friday, he said he not sure that she would live to see election day on November 4.Tax and economy
James Bays, Al Jazeera's correspondent at Obama's rally in Reno, Nevada, said: "They are campaigning on the same territory both in terms of the issues - tax and the economy - and geographically on the same territory.
"They are focusing on this small number of battleground states which are so key at this stage. In most of those battleground states Senator Obama is ahead.
"In [Nevada] he is about three per cent ahead. But that's the margin of error and that's why he is here trying to consolidate his position."
McCain, 72, is scheduled to spend all of Saturday campaigning in New Mexico, where most polls put him trailing for the state's five electoral college votes.
In the last two elections the state has been won by a a tiny margin, with Bush defeating Democrat John Kerry by 0.7 per cent in 2004. However with the 2008 election just 10 days away, most recent polls have McCain trailing Obama by an average of 8.4 per cent.
At a rally in the state, the Arizona senator kept up his attack on Obama's plan to raise taxes for certain sectors of society.
"He believes in redistributing wealth," McCain told about 1,500 supporters. "We've seen that movie before in other countries. That's not America."
"I won't spend nearly a trillion dollars more of your money, senator Obama will and he can't do that without raising your taxes."
Increases and cuts
Obama's proposed tax increase will be placed on people earning an income of more than $250,000 annually - about five per cent of the population. He has backed tax cuts for those who make less.
Obama has said that McCain's tax plans will benefit rich corporations.
Tom Schaller, a professor of political science at the University of Maryland, told Al Jazeera that it was difficult to see how the Republican's could win with their current strategy.
"McCain needs to shift his message back to foreign policy.
"As long as the discussion is the economy that favours Obama."
The economic crisis has apparently bolstered support for Obama as he is viewed as having a greater grasp on such issues.
NBC News has reported that Obama has leads in enough states to put him over the 270 electoral college votes required to win the election.
The US presidential election is decided on a score of electoral votes gained from each state won.
On Sunday, Obama will head to Colorado and McCain to the midwestern state of Iowa.